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by Amin
Today, 2:50 pm
Forum: Off Topic
Topic: How to safeguard my research
Replies: 1035
Views: 77220

Re: How to safeguard my research

Sorry friends, I have been missing my journal for past two days. I have basically almost ceased all activities and am concentrating on improving my program for the evolution of the densities of the SDEs. I have been missing my walk and I leave home in my car once for not more than an hour. And today...
by Amin
February 24th, 2020, 11:13 pm
Forum: Off Topic
Topic: How to safeguard my research
Replies: 1035
Views: 77220

Re: How to safeguard my research

Sorry I missed my daily journal yesterday. I woke up at 11:00 am today(Monday, 24th Feb) as I had slept quite late. I had my breakfast at home and continued to work at home. I made substantial progress in my work regarding the algorithm for evolution of densities of SDEs. At six pm, I left home and ...
by Amin
February 24th, 2020, 3:38 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 877
Views: 84233

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Friends here is the progress on new work. The above algorithm works fine for evolving the densities of SDEs from Z=-5 to Z=1.0 (even in this region I made a slight improvement); However Z>1.0 takes a distortion in tail proportional to total effective volatility of the SDE. I have been working on way...
by Amin
February 22nd, 2020, 8:55 am
Forum: Off Topic
Topic: How to safeguard my research
Replies: 1035
Views: 77220

Re: How to safeguard my research

Sorry, I skipped my daily journal yesterday. My elder sister had arrived from Islamabad on thursday night. She is the one in whose house I live when I am in Islamabad. I did not do any work on my research yesterday. I went with my sister to the psychiatrist doctor at 11:30 am as the doctor had asked...
by Amin
February 21st, 2020, 12:32 pm
Forum: Off Topic
Topic: How to safeguard my research
Replies: 1035
Views: 77220

Re: How to safeguard my research

I want to start writing this post by thanking those great American humans who have tried to protest and stop my persecution on the hands of American mind control agencies. It really gave me a breather to continue my research and be able to devote serious time to my research work. But very recently I...
by Amin
February 21st, 2020, 4:18 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 877
Views: 84233

Re: Breakthrough in the theory of stochastic differential equations and their simulation

While I will continue to work for a genuinely better analytical approximation of derivatives of w with respect to Z. Here is something very simple that improves the above derivatives quite a bit. please replace the line of code dwdZ(wnStart:Nn)=(.5*dwdZ0(wnStart:Nn)+.5*dwdZQ(wnStart:Nn)); with the f...
by Amin
February 19th, 2020, 10:45 pm
Forum: Off Topic
Topic: How to safeguard my research
Replies: 1035
Views: 77220

Re: How to safeguard my research

I woke up after 9:30 am and wasted some time in the home. And then I went out on my car to quickly have some food. I got some good food at the Kitchen cuisine close to Allah-Hu chowk. On the way back I got some NesVita milk in 200 ml servings. When I got home I realized that the Nesvita milk was dru...
by Amin
February 19th, 2020, 9:23 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 877
Views: 84233

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Here is the graph output comparison of true density with Ito-Hermite method density with parameters as in the posted program. [$]\Delta t=.125/16, Tt=128,T=1, x_0=.1250, \ beta_1=0.0, \ beta_2=1.0, \kappa=1.4850,\theta=.125,\sigma=.8,\gamma=.85[$] https://i.postimg.cc/C5XWH6dp/Wilmott-Good-Density-G...
by Amin
February 19th, 2020, 8:07 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 877
Views: 84233

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Ok friends, here is the new progress. Integrating over the subdivisions does not seem to help at all. But when I calculated [$]\frac{\partial \mu(w)}{\partial z}[$] and  [$]\frac{\partial^2 \mu(w)}{\partial z^2}[$] analytically, and tried playing to find an optimal value that could give a good fit t...
by Amin
February 18th, 2020, 7:13 pm
Forum: Off Topic
Topic: How to safeguard my research
Replies: 1035
Views: 77220

Re: How to safeguard my research

I woke up at around 8:00 in the morning. I did not want to do much work in the morning as I had been mostly staying at home working for past three or four days. I decided to go out and drive around a bit in the city. I would have left a little after 9:00 am. I drove to Bahria Town and had my light b...
by Amin
February 18th, 2020, 3:10 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 877
Views: 84233

Re: Breakthrough in the theory of stochastic differential equations and their simulation

I have been working how to calculate derivatives of SDE variable w with respect to Z analytically. Earlier I thought of following the numerical derivatives route but from my past bitter experience these derivatives are extremely bad at the boundaries and 2nd derivative when calculated numerically a...
by Amin
February 17th, 2020, 7:16 pm
Forum: Off Topic
Topic: How to safeguard my research
Replies: 1035
Views: 77220

Re: How to safeguard my research

I woke up after 10:30 since I had slept late. I did a slight bit of work and then went out on my car. I remained outside for about an hour and then came back home. Then I wrote the formulas in my research again in terms of standard gaussian. I also realized the reason for errors in my SDE evolution ...
by Amin
February 17th, 2020, 1:28 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 877
Views: 84233

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Dear friends, I have been thinking about the precise 'cause and effect' that we need to know to get our latest Ito-hermite algorithm working in which we evolve an expanding and drifting SD fractions grid. We divide this expanding and drifting SD fractions grid into subdivisions where center of each...
by Amin
February 16th, 2020, 7:42 pm
Forum: Off Topic
Topic: How to safeguard my research
Replies: 1035
Views: 77220

Re: How to safeguard my research

I woke up at around 7:30 am. And after about half an hour I jotted down some notes in order to copy them here because everyday when I write this journal, usually I am quite sleepy and I just write the few main basic things and forget several incidents that I would otherwise like to mention. I basica...
by Amin
February 15th, 2020, 8:53 pm
Forum: Off Topic
Topic: How to safeguard my research
Replies: 1035
Views: 77220

Re: How to safeguard my research

I woke up at around 8:00 am. After a bit, I started to concentrate on my work. I had enough water and food from yesterday. I basically worked from time to time. I also had a nap for 45 minutes in between. At around 2:00 pm, I went out for twenty-five minutes and take a bit of food and return home. I...
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