SDE Problems

SDE Problems

Mathematical Specification of a SDE Problem

To define an SDE Problem, you simply need to give the forcing function $f$, the noise function g, and the initial condition $u₀$ which define an SDE:

\[du = f(u,p,t)dt + Σgᵢ(u,p,t)dWⁱ\]

f and g should be specified as f(u,p,t) and g(u,p,t) respectively, and u₀ should be an AbstractArray whose geometry matches the desired geometry of u. Note that we are not limited to numbers or vectors for u₀; one is allowed to provide u₀ as arbitrary matrices / higher dimension tensors as well. A vector of gs can also be defined to determine an SDE of higher Ito dimension.

Problem Type

Wraps the data which defines an SDE problem

\[u = f(u,p,t)dt + Σgᵢ(u,p,t)dWⁱ\]

with initial condition $u0$.

Constructors

For specifying Jacobians and mass matrices, see the DiffEqFunctions page.

Fields

Example Problems

Examples problems can be found in DiffEqProblemLibrary.jl.

To use a sample problem, such as prob_sde_linear, you can do something like:

# Pkg.add("DiffEqProblemLibrary")
using DiffEqProblemLibrary
prob = prob_sde_linear
sol = solve(prob)
DiffEqProblemLibrary.prob_sde_linear
DiffEqProblemLibrary.prob_sde_2Dlinear
DiffEqProblemLibrary.prob_sde_wave
DiffEqProblemLibrary.prob_sde_lorenz
DiffEqProblemLibrary.prob_sde_cubic
DiffEqProblemLibrary.prob_sde_additive
DiffEqProblemLibrary.prob_sde_additivesystem