Coupled stochastic differential equation

Asked Nov 22 '20 at 09:56

Active Nov 22 '20 at 20:57

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I am trying to solve the following coupled system of stochastic differential equations:

$\qquad \dot{x}(t)=y(t)\,\eta(t)$
$\qquad \dot{y}(t)=x(t)\,\eta(t)$

$x$ and $y$ are functions to be solved for and $\eta$ is a Wiener process. I think this is a coupled Stratonovich process. I have read the documentation for Stratonovich processes, but it doesn't mention how to solve coupled Stratonovich processes.

I hope someone will be able to help me.

edited Nov 22 '20 at 20:57

m_goldberg

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asked Nov 22 '20 at 09:56

eeqesri

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There are examples in the documentation under Scope->Basic uses. – b.gates.you.know.what Nov 22 '20 at 09:59
oh. i skipped that part. thanks that solves the problem. – eeqesri Nov 22 '20 at 10:07
I have a mathematical question though: I saw some examples in the documentation and there can be terms which are like $x[t]dw[t]$. but from the equation I wrote shouldn't it be more like: $d(x[t]w[t])$? – eeqesri Nov 22 '20 at 10:17
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Seems to be somewhat related to this https://mathematica.stackexchange.com/questions/219515/itoprocess-for-3-coupled-sdes-sourced-by-5-wiener-processes – chris Nov 22 '20 at 10:43
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@chris yes that is very helpful. thanks – eeqesri Nov 22 '20 at 14:00

Coupled stochastic differential equation

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