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by Amin
October 17th, 2019, 3:03 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 823
Views: 64840

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

if Gaussian probability function p(Gaussian) is denoted by [$]pZ()[$] then we could instead simply move our Z grid on each step so that on new grid the new modified Gaussian probabilities are equal to true probabilities as give by [$]p_{true}[$] as [$]Z=pZ^{-1}(p_{true})[$] using inverse of normal ...
by Amin
October 16th, 2019, 3:02 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 823
Views: 64840

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

Today was a slightly better day. I still did not do any work but had some thoughts. Here I put them on paper for friends. We are done with diffusion and translation with respect to Z or B(t). We have to take into account the effect of killing/growth of probability density by Feynman Kac exponential....
by Amin
October 15th, 2019, 12:34 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 823
Views: 64840

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

I have decided to halt this thread for the time being. For reasons, please look at my thread in off-topic. Post 983.
by Amin
October 15th, 2019, 12:31 pm
Forum: Off Topic
Topic: How to safeguard my research
Replies: 982
Views: 62080

Re: How to safeguard my research

I have decided to stop my research on stochastic processes. The city of Lahore is being drugged very fast and it is very difficult for me to do any meaningful research. I have been hit by drugged food multiple times in past several days and  my whole body and head is aching and even passing time bec...
by Amin
October 14th, 2019, 1:43 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 823
Views: 64840

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

An informal update for time being The right evolution equation along the CDF lines incorporating the effect of first and second mode (1st and 2nd equation post 815) is given as [$] X(t+\Delta t)=X(t)+(B(t + \Delta t) -B(t))  {(\frac{\partial X}{\partial B})} + \mu(X) {\Delta t} -2 \sigma(X) \frac{\p...
by Amin
October 13th, 2019, 4:00 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 823
Views: 64840

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

Here are some of my comments on the previous equations and some analogies. Let us suppose we are given an SDE of the form [$]dX(t)=\mu(X) dt + \sigma(X) dz(t)[$] The short term solution to the associated fokker planck given by fourier transform is given as   refrence for the above is (  https://digi...
by Amin
October 13th, 2019, 3:36 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 823
Views: 64840

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

Friends, I have edited equation 6 in post 815 for time being. I will be coming with detailed solution in 2-3 days with analytic calculation of derivatives w.r.t brownian motion.
by Amin
October 11th, 2019, 4:43 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 823
Views: 64840

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

Over the weekend, I will present a detailed method about how to calculate the derivatives of the sort [$]\frac{\partial B}{\partial w}[$] , [$]\frac{\partial ^2 B}{\partial w^2}[$] and [$]\frac{\partial ^3 B}{\partial w^3}[$] analytically. I have worked over the main idea and I am completing the det...
by Amin
October 11th, 2019, 2:09 pm
Forum: Off Topic
Topic: How to safeguard my research
Replies: 982
Views: 62080

Re: How to safeguard my research

I want to tell friends and my well wishers that very recently persecution activity has started in full steam. All the drinks and beverages in the markets in the neighborhood where I live and in closeby neighborhoods are getting thoroughly drugged. Though I have also become extremely careful and go ...
by Amin
October 10th, 2019, 11:20 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 823
Views: 64840

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

I have updated the exposition. I had wrongly equated all of the three independent modes of evolution equations to zero. Sorry, I had not prepared any proper notes for the equations and I was  not careful when I wrote the post. These are three independent modes of evolution dictated by each eigenvect...
by Amin
October 10th, 2019, 8:32 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 823
Views: 64840

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

Friends, here is the new derivation of solution of Fokker-Planck using the derivatives of X(t) with respect to Brownian motion.  Let us suppose we want to solve a general SDE given as [$]dX(t)=\mu(X) dt + \sigma(X) dz(t)[$] The fokker planck equation of this SDE is given as [$]\frac{\partial p(X,t)...
by Amin
October 9th, 2019, 3:59 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 823
Views: 64840

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

I think it would be better to expand the diffusions in terms of derivatives with respect to brownian motion instead of standard normal Because otherwise it is difficult to get something proportional to second hermite polynmial(that is associated with second derivative of the density of normal) on t...
by Amin
October 8th, 2019, 3:18 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 823
Views: 64840

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

I copy the second last equation from the previous post. [$]\frac{\partial [p(Z) \frac{\partial Z}{\partial X} ]}{\partial t} = -\mu(X) (-Z p(Z){(\frac{\partial Z}{\partial X})}^2+p(Z) \frac{\partial^2 Z}{\partial X^2}) - \frac{\partial \mu(X)}{\partial X} p(Z) |\frac{\partial Z}{\partial X}|[$] [$]...
by Amin
October 7th, 2019, 5:38 pm
Forum: Off Topic
Topic: How to safeguard my research
Replies: 982
Views: 62080

Re: How to safeguard my research

Some selected food and water is getting drugged in Johar Town Lahore area where I live. I bought water from a large store during my evening walk. Since I take the same path for walk every time, they knew which stores I can enter. And I bought water from a large store but it was drugged. I drank half...
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