Julia package SDE.jl¶
The package contains the following modules:
- Generate Ito processes and diffusions
- Nonparametrically estimate the drift of a diffusion
- Provides rudimentary finite element methods and Schauder basis for NonparBayes
- Computes the solution of the continuous Lyapunov equation, useful for the generation of linear processes
- Random symmetric, positive definite, stable matrix for testing purposes.
- Homogeneous vector linear processes with additive noise
The producure in
NonparBayes is a Julia implementation of nonparametric Bayesian inference for
“continuously” observed one dimensional diffusion processes with unit diffusion coefficient. The drift
is modeled as linear combination of hierarchical Faber–Schauder basis functions with a Gaussian prior
on the coefficients. This incorporates a Brownian motion like prior on the drift function. The posterior is
then computed using Gaussian conjugacy.
This is work in progress.
I did not introduce type definitions for stochastic processes and use vectors/arrays, so it should be easy do wrap Dataframes around everything. For the meanwhile, I like the natural notation obtained by having just vectors/arrays for dW and dt
N = 100 t = linspace(0., 1., N) dt = diff(t) X = ito(2dt + 2dW1(dt))
Location of the documentation¶