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Questions tagged [stochastic-ode]

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How to determine the order of convergence of the Euler-Maruyama method?

This question is originally posted in Quant.StackExchange but has been unanswered for some time so I ask in here. To make this simple let us consider the Geometric Brownian Motions (GBM). My ...
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0answers
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SDE solver in python: manual determination of integrator step size (dt)

Aim: I am trying to solve a system of SDEs, while using the SDEint package in python 3.x. It is a system of SDEs adapted from and inspired by the Zombie Apocalypse ...
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1answer
74 views

Jump-Diffusion process: practical solver beyond Euler method?

A jump-diffusion process is a stochastic process where both continuous noise (in my case complex Wiener noise $dZ,dZ^*$ such that $dZ^2=dZ^{*2}=0,|dZ|^2=dt$) and discrete Jumps (in my case Poissonian $...
3
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1answer
48 views

Testing Wiener process splitting in adaptive-step SDE integrators

I am investigating various methods for adaptive-step integration of stochastic differential equations and trying to implement them. All of the papers that I've seen (e.g. H. Lamba, J. Comp. App. Math. ...
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1answer
33 views

Open source solver for continuous-time stochastic non-linear DAEs (SDAEs)

I am trying to solve a system of non-linear index-1 DAEs in which the derivatives of the state variables, $x(t)$ are corrupted by additive noise, $w(t)$ (whose co-variance matrix is known). $\dot x(t)...
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1answer
235 views

Easily understandable argument that normal Runge–Kutta methods cannot be generalised to SDEs?

A naïve approach to solving stochastic differential equations (SDEs) would be: take a regular multi-step Runge–Kutta method, use a sufficiently fine discretisation of the underlying Wiener process, ...
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2answers
184 views

What’s so great about derivative-free solvers for SDEs?

I am trying to familiarise myself with SDEs and have been reading a few review papers on the topic. They leave the impression that a great deal of work has been put into solvers that are derivative-...