14 votes
Accepted

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

Let's take a stochastic differential equation: $$ X_t = f(t,X_t)dt + g(t,X_t)dW_t $$ Here's a few different arguments which lead to intuitive understandings of why the mathematics behind the higher ...
7 votes
Accepted

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

I can understand that this property is useful in some applications where the derivative is difficult or computationally infeasible to obtain or does not exist. However, I would not expect such ...
5 votes
Accepted

Stochastic SIR using SDEint python package

This model is implemented using Julia's DifferentialEquations.jl in this tutorial. Here's a version of that code: ...
4 votes

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

I am not an expert in specifically stochastic differential equations, but I would assume that my answer will still be of some value. Computation of the derivative can be challenging, as you mentioned ...
  • 8,461
3 votes
Accepted

Solving an SDE with time-dependent parameter in R

The parameter can be any type, so here I pass in a time-dependent function for p and use it in the differential equation: ...
3 votes
Accepted

Simulate Jump-Diffusion $dX_t = \mu(X_t)dt + \sigma(X_t)dW(t) + \int_{\{|c| <1 \}}g(X_t,c)\tilde{N}(dt,dc) + \int_{\{|c| \ge 1 \}}h(X_t,c)N(dt,dc)$

You can try DifferentialEquations.jl for jump diffusions. It has a tutorial on jump diffusion models: https://diffeq.sciml.ai/stable/tutorials/jump_diffusion/ and more documentation at: https://diffeq....
3 votes
Accepted

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

DifferentialEquations.jl in Julia can do it if you can write it in mass-matrix form. You won't find it mentioned in the tutorial, but you can provide a mass matrix as part of the ...
2 votes

Time independent Runge Kutta integration of SDE

The first method is Euler-Maruyama with its strong convergence of order $0.5$. This can be seen in the difference plot on the right. The step sizes vary with a factor of $4$, while the error does not ...
  • 3,711
2 votes
Accepted

Jump-Diffusion process: practical solver beyond Euler method?

The setup that is used in DifferentialEquations.jl and QuantumOptics.jl is what's known as time-adaptive jumping. It's nice because it allows for jump events to do things like change the number of DEs,...
2 votes
Accepted

Testing Wiener process splitting in adaptive-step SDE integrators

I discuss the method you describe in more detail in this paper (Rackauckas and Nie 2017) as RSwM2. In that paper I am ever so slightly able to detect that it's sometimes doing something wrong, but ...
1 vote

Simulate Jump-Diffusion $dX_t = \mu(X_t)dt + \sigma(X_t)dW(t) + \int_{\{|c| <1 \}}g(X_t,c)\tilde{N}(dt,dc) + \int_{\{|c| \ge 1 \}}h(X_t,c)N(dt,dc)$

In terms of simulating a visual representation of a jump diffusion model,matplotlibprovides excellent diagraming capabilities. Here is an article outlining a use ...

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