CODEWITHSUNDEEP
pythonnumpydifferential-equationsrunge-kuttastochastic
user10367182
user10367182

Reputation:

Deterministic and stochastic part of an equation

I'm on the lookout for a numerical method that can solve both a deterministic and stochastic equation. In the deterministic case, I know that a fourth order RK method is a valuable one, very effective. Unfortunately, there has not been applied to stochastic equations successfully (at least as far as I know).

Now what I want to know is if a numerical method that can solve both equations (roughly I mean, in comparison to the analytic solutions) exists and, in that case, what would be. A stochastic equation analytically solvable would be the Black-Scholes one, for instance.

Upvotes: 0

Views: 437

Answers (1)

Chris Rackauckas
Chris Rackauckas

Reputation: 19152

There are methods for solving these kinds of equations in DifferentialEquations.jl. Stochastic differential equations are a form of mixed deterministic and stochastic equation and solving them is shown in the SDE tutorial. Mixing discrete stochasticity with deterministic equations is shown in the jump equation tutorial. While written naively in Julia, it is accessible in Python via the package diffeqpy. Notice that this has some example stochastic differential equations in the README.

Upvotes: 1

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