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by Amin
July 8th, 2020, 1:16 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 948
Views: 111017

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

I am quickly posting this code which is based on derivatives derived from the analytic solution of Fokker-Planck equation. I works reasonably well only and accuracy deteriorates as value of kappa increases to larger values but this is only intermediate code before the final version. I will get an a...
by Amin
July 8th, 2020, 3:16 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 948
Views: 111017

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

Sorry for the delay in my post. I am not posting a new program but I would describe how I solved the equation using both forward and backward differences. It is very simple. I just solved the whole barebone equation with forward differences and then solved the whole barebone equation with backward ...
by Amin
July 7th, 2020, 1:30 am
Forum: Off Topic
Topic: How to safeguard my research
Replies: 1142
Views: 104624

Re: How to safeguard my research

I had promised friends that I would tell them in detail what happened when I was in detention. But I have so little energy and drive that it is very hard to get myself to sit down and write everything and I have been delaying it. After returning from detention, I have all my meals at home and, obvi...
by Amin
July 4th, 2020, 11:05 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 948
Views: 111017

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

I want to make this addition to my past few posts in recent days about appropriate calculations of barebone(first derivatives solution) solution to fokker-planck equation. What I wrote in previous few posts was the right calculation of first derivatives using adjacent "backward finite difference de...
by Amin
July 2nd, 2020, 2:32 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 948
Views: 111017

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

Please read the last two posts on previous page since they have far more significance than this post. Sorry, I forgot to post this dependency function for the program in previous post. function [y0] = InterpolateOrderN6(N,x0,x1,x2,x3,x4,x5,x6,y1,y2,y3,y4,y5,y6) if(N==6) y0=(x0-x2)*(x0-x3)*(x0-x4)*(...
by Amin
July 2nd, 2020, 1:24 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 948
Views: 111017

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

Here is the matlab program for the above barebone first order solution of FPE. function [TrueMean,ItoHermiteMean,y_w,fy_w,wnStart] = FPERevisited02() %Copyright Ahsan Amin. Infiniti derivatives Technologies. %Please fell free to connect on linkedin: linkedin.com/in/ahsan-amin-0a53334  %or skype ahs...
by Amin
July 2nd, 2020, 11:40 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 948
Views: 111017

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

In my earlier Ito-hermite evolution equations, the barebone (part of the solution equation that depended only on first derivatives without including the effect of second and higher derivatives) solution of general SDEs was borrowed from brownian motion solution equation. Brownian motion solution eq...
by Amin
July 1st, 2020, 1:59 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 948
Views: 111017

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

I have been trying to mould the evolution equation for Fokker-planck PDE into a form that new evolution equation does not depend upon distance from the mean of the SDE distribution but rather depends upon distance from the next/adjacent grid point so we can use local derivatives for the evolution e...
by Amin
June 28th, 2020, 10:25 am
Forum: Off Topic
Topic: How to safeguard my research
Replies: 1142
Views: 104624

Re: How to safeguard my research

It has already been so many days since the end of my detention at a psychiatric facility and I wanted to write all details of the time I passed in detention. But weather in Lahore is so hot and it is virtually impossible for me to do anything meaningful. I will start writing all daily journals with...
by Amin
June 27th, 2020, 3:57 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 948
Views: 111017

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

I am posting a different program which is also very good. But wonderful thing is that in this program most derivatives are almost the same as the ones analytically calculated as in post 920. I have added extra multiplication with second or first hermite polynomial and scaling constant is still arbit...
by Amin
June 26th, 2020, 3:30 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 948
Views: 111017

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

Please replace the terms in posted program with these new terms: CTerm(wnStart:Nn)=(.25*d2wMu0dtdw2(wnStart:Nn).*dwdZ(wnStart:Nn).^1.*Z(wnStart:Nn)/sqrt(2.0) - ...           1*dwMu0dtdw(wnStart:Nn).*d2wdZ2(wnStart:Nn));        Correction1(wnStart:Nn)=-.925/(22/7)^2.*CTerm(wnStart:Nn).*H2(wnStart:Nn)...
by Amin
June 25th, 2020, 5:54 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 948
Views: 111017

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

Here I am posting the new improved program that I used to create the above graphs. I continued to change NoOfBins parameter used for graphing. Here is the new program. function [TrueMean,ItoHermiteMean,MCMean] = ItoHermiteWilmottMeanCorrected04WNew02(x0,theta,kappa,gamma,sigma0,T) %Copyright Ahsan ...
by Amin
June 25th, 2020, 4:25 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 948
Views: 111017

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

I am posting a few graphs of mean reverting SV type SDE densities with my new version of SDE density evolution program. I have posted a graph for each SDE density focusing on the main body of the SDE density followed by another graph focusing on the tail of the same SDE density. SDE parameters are ...
by Amin
June 25th, 2020, 10:13 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 948
Views: 111017

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

Friends, I have been playing with my Ito-hermite version of SDE density evolution program. Earlier programs were good with the main body of the distribution but off in the right tail even with mean correction. But I have been able to make some changes to the earlier algorithm so it works great even...
by Amin
June 24th, 2020, 4:19 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 948
Views: 111017

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

Removing the zero mean hermite polynomials would give us better accuracy since usually our grid would be sparse and non-symmetric where including these hermite polynomials in our mean calculations could add to inaccuracies Sorry for bad use of the word sparse. What I basically meant was that the tr...
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