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I have a system of stochastic differential equations that I would like to solve. I was hoping that this issue was already address. I am a bit concerned about constructing my own solver because I fear my solver would be too slow, and there could be the issues with numerical stability.
Is there a python module for such problems?
If not, is there a standard approach for solving such systems.
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Differential equations are solved in Python with the Scipy. integrate package using function odeint or solve_ivp. t: Time points at which the solution should be reported. Additional internal points are often calculated to maintain accuracy of the solution but are not reported.
We multiply both sides of the differential equation by the integrating factor I which is defined as I = e∫ P dx. ⇔ Iy = ∫ IQ dx since d dx (Iy) = I dy dx + IPy by the product rule. As both I and Q are functions involving only x in most of the problems you are likely to meet, ∫ IQ dx can usually be found.
One approach for solving the stochastic differential equation given by equation (6.2) is using the Feyman-Kac theorem. More precisely, by the change of variable method,23 a partial differential equation equivalent to the stochastic differential equation (6.2) can be achieved.
There is one: http://diffusion.cgu.edu.tw/ftp/sde/
Example from the site:
""" add required Python packages """
from pysde import *
from sympy import *
""" Variables acclaimed """
x,dx=symbols('x dx')
r,G,e,d=symbols('r G epsilon delta')
""" Solve Kolmogorov Forward Equation """
l=sde.KolmogorovFE_Spdf(r*(G-x),e*x*(1-x),0,1)
sol=l.subs({e:r*d})
pprint(sol)
The link in the accepted answer no longer functions. There is also sdeint:
https://pypi.org/project/sdeint/#description
Which was released a few years after the accepted answer and looks to be in semi-active development. A second example in the documentation has a system of SDE with constant coefficients. I am unsure if they have support for more complex SDE systems.
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