Friends, mind control agencies were able to drug my food today. I was passing by General hospital on Ferozpur road and decided to eat at hospital canteen. I forgot to notice that canteen was right at the door and had a direct entrance on main road outside the hospital. While taking parking token at the gate where there were about five motorcycles ahead of me in the line. It took me about two minutes to get the token.
I believe while I was in line for token, somebody entered the canteen from outside gate and drugged the food.
After eating drugged food, my conception of reality changed and I started to see differently from my eyes. I could feel that I was missing something in my brain. I washed my head right there and had some coffee(merely by mixing it in room temp water).
Only when I left the hospîal, I realized that its canteen had an entrance outside the gate of hospital on the main road.
I was slightly getting worried but I kept myself totally calm with some effort.
In a little bit, I bought some traditional sweets and sweet milk from random places on small streets branching out of ferozpur road. I was a bit better after that.
Then I drove my bike on narrow streets on one side of ferozpur road where I had never been before. I believe there was no mind control infrastructure in those very poor neighborhoods. I felt quite better after that. I also continued to wash my head and do tooth brush there.
Finally I came back. I am better now but feel something is still missing in my brain. They continue to pull drugs from food in my stomach towards the brain to successfully block neurotransmitters that come back again and again.
After coming back, I mixed a lot of psyllium husk, I had boùht on the way, with water to cleanse my stomach and intestines.
I have an injection due tomorrow so next few days can be difficult.

Friends, I bought a totally new computer a few weeks ago but  Pakistan army on behest of corrupt American army scum continues to play openly with my computer in my absence. They have completely muted sound on my computer (possibly through playing with the hardware). I tried to restore the volume from settings everywhere but it simply does not work and there is absolutely no sound in my computer now. It was working very well just a few days ago.

My mind control also continues unabated and there is extreme urgency (and huge increase of efforts) among mind control infrastructure in Pakistan to somehow retard me. It is becoming more and more difficult to be able to get good food in the city. They have been viciously trying to retard me and drug my food in past few days and I expect this to continue for many coming weeks. I am trying to hold on but I do not know how long could I last since scale of Pakistan army people following me all the time is simply huge.

I want to request European Embassies in Pakistan to please step forward and tell Pakistani people in their circles the whole truth about mind control and also force government and military of Pakistan (that is puppet extension of corrupt American defense) to end my mind control and mind control of other people in Pakistan. 

I want to say to American friends that I tried to tell the truth about bad groups in United States for more than one and a half decade(s) and I expect that a lot of people know that I was speaking the truth. Good Americans are a smart people and I am sure they will try to take exactly right decisions for their nation and for rest of the world and they would make sure that cruel injustice of mind control and related injustices from corrupt US defense end forever. 

I have run my part of the race (even though I am ready to run another leg if things do not get better) and now baton is in hands of Good and patriotic American people to make good and wise decisions about what is best for their country and best for rest of the world to end the corruption in US defense and end machinations of bad people and also make sure that bad people do not start machinating again. I just want to request good American people to know that there could be attempts by bad people to make some possible settlement only to start machinating again(at a possibly decreased scale) when the whole thing goes out of limelight.

Friends, my research work for finding volatility dependent coefficients of hermite series of asset by hermite regression is going well but rather slowly due to all the problems created by mind control agencies. I have constructed a variable spacing grid for stochastic volatility. And then calculated first eight moments of dependent asset for each of the voltility cell  (This calculation is done directly from data by using asset paths that lie in each stochastic volatility cell instead of integrating over probability distributions). In order to make sure there are enough data memebers/paths of asset that lie in the volatility cells that are in extreme tail, I paired six volatility cells in right tail to form three resulting cells in modified tail so that asset density per cell increases in the tail for better calculation of moments.
I am only using fifty grid cells for volatility but this seems enough since grid is variable.
Next step is to calculate asset Z-series for each of the volatility cell but this is easy since we have already calculated moments of asset associated with  each volatility grid cell.
After that I would continue with regressing hermite polynomials of coefficients of all of the asset Z-series on hermite polynomials of volatility.

I am worried that agents who come to my house might permanently damage my new computer. As I told friends that they had damaged my last computer I bought with very little money I had and that cost me about a thousand dollars. 
They are also known for taking liberties with many of my old computers( I have bought about 8-10 laptop computers since 2010) like damaging the keyboard buttons, damaging usb ports and the speakers and sound system (on the previous old computers).
They have already disabled the sound system(I believe through unplugging the hardware) of my new computer and there is absolutely no sound on the new computer I bought a few weeks ago. I had described it in a post earlier as well.

Friends, my research is going well. I have been able to make a variable grid in both volatility and asset. So asset grid is different for each grid point of stochastic volatility associated with it. 
Obviously the original target of research is to find the volatility dependent coefficients of the asset Z-series and I am continuing work towards that but as a quick byproduct of the research, I was able to modify the earlier program that constructed the numerical density of bivariate product of asset and volatility. In this new program the calculation of 2D Hermite Series is done on a coarse grid that is variable in both stochastic volatility and asset. Once the 2D Hermite series has been calculated, it can be used to project the analytic density on a very refined grid that is uniform both in stochastic volatility and asset.
I will try to post this interim program with above analytics tomorrow. 

Friends, there can still be many other ways to find a two dimensional Z-series/Hermite Series of a bivariate random variable. 
For example if we want a bivariate Z-series/Hermite series of stochastic volatility and asset, in a monte carlo setting, we can calculate all moments and cross moments up to a certain order(for example till eight order of moments) and then use a procedure similar to what we devised for calculation of a single dimensional hermite series from its moments. (We can always calculate 2D density of single asset from the bivariate density of stochastic volatility and asset.)
We can have an initial iterative procedure that would approximately calibrate(just like we did in one dimensional Z-series) cross moments on appropriate products of hermites and 1D moments on univariate hermites of same order. I am sure it is very do-able. 
However we had a large number of calculations even while calculating moments of single dimensional Z-series and calculations of 2D hermite series would approximately be roughly a square of the order of effort required for a single dimensional Z-series. It would be interesting to find a most efficient algorithm that actually calculates all 2D moments and cross moments for a 2D Z-series and matches it input values of cross moments. If we can do it, I believe this can be most stable way to deal with the problem that could also tackle dependent and correlated bivariate variables. 
Why do we have fast computers of today if we cannot solve these 2D or 3D random variable Z-series calculation problems on them?
Though we have started work on 2D random variable models, I believe that it will take many more months (possibly up to six months) for things to become perfectly clear about what is the best approach to tackle 2D random variable models and find their Z-series and do appropriate analytics like hermite regressions on them. 
I am really under pressure these days because my persecution and attempts at drugging my food in the city have sharply increased in past one week. But I really hope that this problem would settle somewhat in next few weeks. I really want to be in peace and try to focus on doing good research about the problem of calculation of 2D Z-series in the best and most reliable way and also be able to do other analytics with the method like hermite regressions and other related things.

Friends, even though I do not believe in religion, I am probably still classified by many others as a non-practicing muslim. I want to tell friends that like most other muslims, I totally condemn violence started by Hamas. In twenty first century human civilization, there is no place for violence and brutality like this and this should end forever. 
But, instead of increasing vicious circle of violence, there have to be serious attempts at bringing both parties in the middle east conflict on the table. America, Britain and Europeans should force Israel to join the talks as Saudi Arabia and Qatar should force Hamas and other Palestinians to start talks with Israelis (or end funding of Hamas and Al-Fatah if they do not join the talks. They should also make sure and audit that their funding is only spent on humanitarian and civilian needs and not on missile programs and also tell Palestinians that all funding will stop in case of any future violence.)
Present vicious round of violence should make it clear to all the responsible regional and world powers that in order to end violence forever, there should be a lasting solution to middle east conflict. A solution that is just, fair and amicable to both parties. If the world powers and regional powers do not play their role and ignore the matter again, the circle of violence will become even more vicious after it. America and Europeans should force Israel for a reasonable settlement as Saudi Arabia and Qatar should force Palestinians to accept a reasonable solution to the problem.
About two decades ago, there was huge activity by world powers to find a settlement of the conflict but later every major country accepted the status quo and there were just only lukewarm efforts to bring Israelis and Palestinians together for talks. If the momentum of talks, that was there some two decades ago, had continued, I am sure there would have been a settlement of the matter and present violence could have been avoided and both Palestinians and Israelis would have been living with their human dignity intact. Violence and wars have no respect for human dignity.
I would also ask people to not let the middle east violence overshadow our efforts to end cruel mind control in America and all other countries. As I have explained several times earlier on this forum, my struggle was never against jews at all. It was only against those people who connive together to bribe American defense in order to retard intelligent people they do not like and many of those people happen to be jews so I had to mention this. 
I totally respect good jews who abhor cruel mind control by the billionaire Godfather of mind control and his rich cohort and have nothing to do with the activity of the billionaire Godfather and his cohort.

Friends, weather here in Lahore is better but still warm. However it is not that hot now that it was a month or two ago. I also have some good coffee so I want to make the most out of my time in terms of trying to do better research. 
I noticed whenever data is very noisy, our original method to calculate Z-series from moments becomes non-robust. For example, I tried it on asset distribution associated with each volatility grid cell but with very poor and non-robust results. Method works well when we have very well defined precise moments as we find out of analytic solution of SDEs but when data and resulting moments are very noisy, the method sometimes becomes very poor.
I am trying two other explicit methods to fit the data directly to find its Z-series and I hope these new methods will be far more robust. I will give details in a few days but I am not working with inner product method for these two new approaches.
I am a bit excited about the new possibilities and I really hope that my work goes well. As soon as I have more results and I could verify that the new methods work, I will post the details here on the forum. This is a small diversion from the earlier research project but it is required to make the project code work smoothly and in a few days, we will restart the work towards the main research topic but work in this diversion will be very helpful towards that.
Only if I did not have to waste a few hours everyday trying to get good food and water, I would have totally enjoyed this time to try doing good research.
I will post the details of new methods hopefully in another two days. 

Friends, There is a very huge increase in my persecution and attempts to drug my food in the city over past two weeks. Both evil jews and corrupt American defense consider me responsible for the awareness in a lot of good people about their nexus. And both evil jews and corrupt American defense bitterly want to continue their symbiotic relationship and really want mind control of talented people to continue at all cost. Both are convinced that  they can dupe good American people to say that they want mind control to end but only want to keep retarding intelligent and talented people in the future. They consider me an obstacle in their future plans and know that the truth about mind control will remain in limelight as long as I continue my research and keep posting it on internet.
They either want me to end my research forever or want to somehow keep it away from public. I think they plan to accomplish this by drugging my food so I lose perfect balance of my brain and then everybody would suggest that I am having mental problems and I had schizophrenic history so I will be detained again. And the new psychiatric doctor would suggest that reason for my mental disease is that I am too attached to me research and in order to become mentally healthy, I must end my research in mathematics.
So this way they would be able to stop my research and the whole thing will go out of limelight and then evil jews and corrupt American defense would increase mind control slowly again.
Another possibility they have is to let me work full time somewhere so my research would be my employer's property and I would never post anything after that on wilmott or elsewhere on internet. 
I have plans to work in a few months (since I will have to earn money) but I just want to take some consulting work related to my research in a way that it does not hinder my public research at all.
Bad People who have benefitted from mind control truly want it to continue one way or other and they really think that it would be difficult as long as I keep posting my research on internet and the whole thing will remain in limelight. Therefore American defense has hugely increased attempts to drug my food in the city on an unprecedented scale I have rarely seen before. They are drugging all of food, beverages and water in the city. There is no large brand of water that is manufacturing good water now. All the big brands are manufacturing drugged bottled water in the city. So I have to be extremely careful in getting good food and water. There were some beverages and juices that were good but most of them are turning into drugged juices and beverages now since recently manufactured supply that enters the market is drugged at manufacturing source. 

Friends, I have been able to get very reasonable estimates of conditional Z-series of asset for every Stochastic volatility subdivision. The densities found from Z-series coefficients are quite robust, stable and reasonable and seem good when graphed. 
I will give details of the method later but I used a variant of a method that I had earlier posted on this thread before. I will give details later but briefly the data is first sorted. And then normal density is divided into equal probability subdivisions equal to number of data members(in our case number of asset paths that fall in a particular volatility grid.) We call this ideal normal density. From this density, we find the value of Z associated with each sorted data member. And then the data members  are regressed on values of hermite polynomials found from Z associated with each data member. I tried to match first four moments of the subdivisions so that moments of our ideal density match with true normal density. This gives very robust results for noisy data where our original method of finding Z-series from values of moments fails.
Now I will start working on finding Z-series of each of the eight coefficients of asset across different grid cells of  of stochastic volatility. And then hermite regress it on stochastic volatility to find a single 2D Z-series from which we can get a good estimate of conditional value of asset after substituting the value of V in the 2D Z-series. I hope that the whole work goes well and we would be able to finish it in a few days or possibly in 2-3 weeks.

Friends, I have been able to write a first prototype program about the conditional density research that works well. In the new program, I used monte carlo to create generate joint paths of stochastic volatility and asset. Then I divided the volatility density into forty subdivisions and found conditional density for asset associated with each subdivision. I, then, found the univariate Z-series of each of these asset densities associated with different volatility grid points/subdivisions. The coefficients of all of these subdivisions are different and slightly noisy.  These coefficients can be represented as c0(1:N), c1(1:N), c2(1:N) and so on when there are total N grid points for volatility Then I took each coefficient across all asset Z-series , for example c0(1:N) and then c1(1:N) and continued to c5(1:N), ( I took only six coefficients since terminal time was only two years and I thought that 5th order Z-series will suffice for short maturity.)

Please note that these coefficients of asset Z-series are conditional on stochastic volatility grid. Finally I constructed a Z-series of each of these six coefficients of asset Z-series as a function of stochastic volatility as

[$]c_0(Z_v) \, = \, c_{00} \, + \, c_{01} \, Z_v \,+ \, c_{02} \, {Z_v}^2 \, + \, c_{03} \, {Z_v}^3 \, + \, c_{04} \, {Z_v}^4 \, + \, c_{05} \, {Z_v}^5 \,[$]
[$]c_1(Z_v) \, = \, c_{10} \, + \, c_{11} \, Z_v \,+ \, c_{12} \, {Z_v}^2 \, + \, c_{13} \, {Z_v}^3 \, + \, c_{14} \, {Z_v}^4 \, + \, c_{15} \, {Z_v}^5 \,[$]
[$]c_2(Z_v) \, = \, c_{20} \, + \, c_{21} \, Z_v \,+ \, c_{22} \, {Z_v}^2 \, + \, c_{23} \, {Z_v}^3 \, + \, c_{24} \, {Z_v}^4 \, + \, c_{25} \, {Z_v}^5 \,[$]
[$]c_3(Z_v) \, = \, c_{30} \, + \, c_{31} \, Z_v \,+ \, c_{32} \, {Z_v}^2 \, + \, c_{33} \, {Z_v}^3 \, + \, c_{34} \, {Z_v}^4 \, + \, c_{35} \, {Z_v}^5 \,[$]
[$]c_4(Z_v) \, = \, c_{40} \, + \, c_{41} \, Z_v \,+ \, c_{42} \, {Z_v}^2 \, + \, c_{43} \, {Z_v}^3 \, + \, c_{44} \, {Z_v}^4 \, + \, c_{45} \, {Z_v}^5 \,[$]
[$]c_5(Z_v) \, = \, c_{50} \, + \, c_{51} \, Z_v \,+ \, c_{52} \, {Z_v}^2 \, + \, c_{53} \, {Z_v}^3 \, + \, c_{54} \, {Z_v}^4 \, + \, c_{55} \, {Z_v}^5 \,[$]
Equations (A) -- parametric form of Z-series coefficients conditional on volatility

Z-series of asset, in stochastic volatility model, conditional on stochastic volatility will then be given as

[$]X(Z_x,Z_v) \, = \, c_{0}(Z_v) \, + \, c_{1}(Z_v) \, Z_x \,+ \, c_{2}(Z_v) \, {Z_x}^2 \, + \, c_{3}(Z_v) \, {Z_x}^3 \, + \, c_{4}(Z_v) \, {Z_x}^4 \, + \, c_{5}(Z_v) \, {Z_x}^5 \,[$]

In order to find Z-series of asset conditional on a particular stochastic volatility from Equations (A), we only need to substitute the value of [$]Z_v[$] associated with that stochastic volatility subdivision on the stochastic volatility grid. I still have to see if the same algorithm would work for correlated SV models.

Finally, I compared the conditional asset density constructed from original noisy conditional Z-series that was calculated separately for each of the stochastic volatility grid points with the conditional asset density constructed from the above smooth universal expansion(after substituting the conditional value of Z_v associated with particular volatility subdivision in Equations(A)) of each coefficient as given by Equations(A) and found that match between conditional densities from both Z-series, numerically calculated and parametrically calculated, across all of the volatility grid points was very good.

I will be posting some graphs showing this comparison later today.

I want to continue making more changes and will post the program at the end of weekend or possibly on Monday.  

Friends, here are some graphs that compare the conditional density of asset generated from individually calculated Z-series VS a universal analytic Z-series with parameterized coefficients as described in previous post.
The SDE parameters are on the title. In the title, I have also given conditional value of stochastic volatility V and associated Zv. From this Zv, you can easily tell the value of CDF of SV where the conditional density of asset is calculated.
You can see that match between both types of graphs is perfect between Zv=-2 to Zv=+2. In the tails, I think analytical universal Z-series with parameterized coefficients is better. In the next version, I will also add a totally numerically calculated density for reference as well for comparison.
Here are the graphs.
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Just to make it easier for friends to find context of SDE parameters in the title of graphs in previous post. The relevant SDEs are

Volatility and asset SDE equations are
Vt(0)=V0;
dVt=kappaV *(thetaV - Vt )*dt+sigma0 * Vt^gamma * dz1(t)
Xt(0)=X0
dXt=sigma1* Vt^gammaV * Xt^gammaX *dz2(t);

Friends, I went ahead and tried the graph of bivariate density of Asset and Stochastic volatility(even though it might not be needed and only density of X might be required)  that we were trying earlier with these new analytic universal coefficients that are dependent on volatility. And the results are far better. Earlier we were not being able to capture the shape of graph close to zero but now the shape is properly captured. I have shown the difference of numerical and analytic densities(which are slightly different very close to zero).
After every 2D graph from numerical density follows a graph with analytic density from similar angle so that viewers can compare both of them.
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Friends, I might have to be busy tomorrow with family errands so I will post my matlab programs on Monday.
There is a lot of interesting things we can do with the basic work I have done. For example, I just calculated present distribution of X given the value of volatility. But we could have just equally found the future one or two or three years ahead distribution of asset given present volatility with exactly the same algorithm.
Next step would be to find the conditional density of asset some years/time ahead given both volatility and asset value at current/future time.
Just like we found coefficients of Z-series that are dependent on just one variable that is stochastic volatility, interesting thing would be to parametrize coefficients of a Z-series when the coefficients themselves depend on more than one variable for example two, three or four possibly correlated variables analogous to coefficients depending upon several features as we have in machine learning. 
But we will have to do a lot of steady work to be able to do that.