Julia package SDE.jl

Layout

The main module

SDE

Simulate diffusion processes in one or more dimension. Especially simulate vector linear processes / Ornstein-Uhlenbeck processes Monte Carlo sample diffusion bridges, diffusion processes conditioned to hit a point v at a prescribed time T Functions for transition density, mean and covariance of linear processes Perform Monte Carlo estimates of transition densities of general diffusion processes

with a Submodule

SDE.Schauder

To nonparametrically estimate the drift of a diffusion with unit diffusion coefficient using a Schauder wavelet “basis”

The package contains the additional modules:

Diffusion

Alternative API to generate Ito processes and diffusions

Randm

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

Method

The producure in SDE.Schauder 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.

Location of the documentation

https://sdejl.readthedocs.org

Contents:

• SDE
  • Miscellaneous
  • Stochastic Processes
• Module Schauder
  • Introduction
  • Reference
  • Introduction
  • Optional additional basis functions
  • Reference
• Module Diffusion
  • Introduction
  • Reference
• Module Randm
  • Introduction
  • Reference

Indices and tables

• Index
• Module Index
• Search Page