Julia package SDE.jl

Layout

The package contains the following modules:

Diffusion

Generate Ito processes and diffusions

NonparBayes

Nonparametrically estimate the drift of a diffusion

Schauder

Provides rudimentary finite element methods and Schauder basis for NonparBayes

Lyap

Computes the solution of the continuous Lyapunov equation, useful for the generation of linear processes

Randm

Random symmetric, positive definite, stable matrix for testing purposes.

LinProc

Homogeneous vector linear processes with additive noise

Method

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.

Data structures

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

https://sdejl.readthedocs.org

Contents:

• Module Diffusion
  • Introduction
  • Reference
• Module Schauder
  • Introduction
  • Reference
• Module NonparBayes
  • Introduction
  • Optional additional basis functions
  • Reference
• Module Lyap.jl
  • Documentation
  • Reference
• Module Randm
  • Introduction
  • Reference
• LinProc
  • Introduction
  • Reference

Indices and tables

• Index
• Module Index
• Search Page