Re: Stochastic Differentail equations

• To: mathgroup at smc.vnet.net
• Subject: [mg19527] Re: Stochastic Differentail equations
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Sun, 29 Aug 1999 17:21:25 -0400
• Organization: Universitaet Leipzig
• References: <7q9ghb\$o4l@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Dimitris,

stochasitc differential equations need very special numerical methods.

The typical way in physics ist to make several assumptions about the
propertiers of the noise (spectral function ..) and obtain a partial
diffential equation. The Fokker-Planck equation is the most popular
result.

An ordinary differntial equation solver make several assumptions about
the
derivatives of the rhight hand side. None of these assumptions are valid
for equations with a random variable inside.

I remember some Physical Review articles about the numerical simulation
of ode's with a stochasic rhs. Mail me if I should search for on or two
references.

NDSolve[] uses high order methods to solve the differential equations
and
it needs that the derivatives of orders >3 exist.

Hope that helps
Jens

Dimitris Kugiumtzis wrote:
>
> I am not a regular reader of this newsgroup, so no flames if you
> find the question too simple or often repeated.
>
> I could not find in Mathematica how one can insert random components
> in the differential equations, when one uses NDSolve (giving rise
> to stochastic equations or as often referred to dynamic noise in the
> generated data). I am thinking something like for example
> x'[t]== -(y[t] + z[t])+Random
> where, the derivatives of y and z are defined accordingly (imagine
> for example the Lorenz equations in Mathematica with noise).
>
> If anyone can add something I would appreciate.
>
> Dimitris
>

```

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