Posted by: phedrick | December 7, 2008

## The Stochastic Group

Everyone who wants to read about stochastic groups should really read David G. Poole’s article on the subject. I have posted my review of the article right here. https://math152.wordpress.com/2008/12/07/the-stochastic-group/math152_reading_project1/

## Responses

I’m curious why it’s called the Stochastic Group? Do you know? I assume that each column adding up to 1 has something to do with probability, but I’ve never come across this before.

2. Dear All,

I am interested to the topic of stochatic phenomenon especially in order to explore the corrosion mechanism in nano stuctures to support my research group (at my Dept of Physics, Sepuluh Nopomber Institute of Technologi (ITS) Surabaya, Indonesia) in developing Nano Technology at my country.

You know one of stochastic model that has been commonly used for the purpose is in the following nonlinear first order differential equation driven by white noise.

dy/dt+py=Qy^3 + Acos(2Пft)+δ(t-t’)

where δ(t-t’) is white noise mentioned. Of course imposible to obtain analytic solution of the above model. But I believe analytic solution of Ordinary part of the DE will help in creating accurate solution of the stochastic model.

Recently I have been developing a new method so-called SMT (stable modulation technique) for solving first order ordinary differential equation (ODE) based applying a new modulation scheme that I introduced as stable modulation in which solution of linear solution part of the ODE is substituted into amplitude of the nonlinear solution part. Here, solution of the nonlinear part must be written in a modulation function AF(A) that it’s amplitude A also including at the phase function. A. The SMT succesfully in solving the general Bernoulli Differential Equation (BDE) dy/dx+p(x)y=Q(x)y^n, where n±1 oor another ODE that can be transformed into the BDE. As I inform in this forum previously, the utilize of SMT has been posting at http://eqworld.ipmnet.ru/forum/viewtopic.php?f=2&t=34&start=20.

Now, I invite you to collaborate with me especially to develop the SMT for solving the general of inhomogenous of BDE dy/dx+p(x)y=Q(x)y^n + f(x), where f(x) is arbitrary force function.

Okay, I wait you all who are interested to my purpose. You contact me via email at aliyunus@rohedi.com, or by leaving some comments at my website http://rohedi.com and/or at my wordpress http://rohedi.wordpress.com.

Thank you very much for your attention.
My best Regards,

Rohedi.

3. Dear All,

I am interested to the topic of stochastic phenomenon especially in order to explore the corrosion mechanism in nano structures to support my research group (at my Dept of Physics, Sepuluh Nopomber Institute of Technologi (ITS) Surabaya, Indonesia) in developing Nano Technology at my country.

You know one of stochastic model that has been commonly used for the purpose is in the following nonlinear first order differential equation driven by white noise,

dy/dt+py=Qy^3 + Acos(2Пft)+δ(t-t’)

where δ(t-t’) is the white noise mentioned.

Of course imposible to obtain analytic solution of the above model. But I believe analytic solution of ordinary part of the DE will help in creating accurate solution of the stochastic model.

Recently I have been developing a new method so-called SMT (stable modulation technique) for solving first order ordinary differential equation (ODE) based applying a new modulation scheme that I introduced as stable modulation in which solution of linear solution part of the ODE is substituted into amplitude of the nonlinear solution part. Here, solution of the nonlinear part must be written in a modulation function AF(A) that it’s amplitude A also including at the phase function. A. The SMT succesfully in solving the general Bernoulli Differential Equation (BDE)

dy/dx+p(x)y=Q(x)y^n, for n≠1

or another ODE that can be transformed into the BDE. As I informed in this forum previously, the utilize of SMT has been posted at http://eqworld.ipmnet.ru/forum/viewtopic.php?f=2&t=34&start=20.

Now, I invite you to collaborate with me especially to develop the SMT for solving the general of inhomogenous of BDE:

dy/dx+p(x)y=Q(x)y^n + f(x), for n≠1

where f(x) is arbitrary force function.

Okay, I wait you all who are interested to my purpose. You can contact me via email at aliyunus@rohedi.com, or by leaving some comments at my website http://rohedi.com and/or at my wordpress http://rohedi.wordpress.com.

Thank you very much for your attention.

My best Regards,

AFASMT/Rohedi.

4. Hi,

http://eqworld.ipmnet.ru/forum/viewtopic.php?f=2&t=34&start=30

there is an apportunity to collaborate in developing the SMT to solve the key mathematics model of developing Nano Technology,

dy/dx+p(x)y=Q(x)y^n + f(x) , n≠1

5. Next, if all of you have spare time please visit to this address:

http://castingoutnines.wordpress.com/2007/11/09/i-heart-60s-era-math-books/#comment-17307

On the blog math I also post some related ordinary differential equation that commonly become an ordinary part of stochastic differential equation. For instance, the following form

dy/dt=p(t)y^2+q(t)y+r(t)+δ(t-t’),

where dy/dt=p(t)y^2+q(t)y+r(t) called as the general Ricatti differential equation. Do you know how to create the exact solution of the Ricatti’s DE?.

Thx.
Denaya Lesa.