Gaussian Process Approximations of Stochastic Differential Equations

Posted in Science on August 22, 2008


Gaussian Process Approximations of Stochastic Differential Equations

It is well known that certain classes of Gaussian process arise naturally as solutions to stochastic differential equations, for example the Ornstein-Uhlenbeck process arises as the stationary solution of a simple linear stochastic differential equation. In this work we introduce some initial results on the approximation of the solution of general stochastic differential equations by Gaussian processes. We employ a variational framework, where we seek a Gaussian process approximation to the posterior distribution of the state of a system whose dynamics are governed by a stochastic differential equation. The application for this work is approximate inference within stochastic dynamic models, in particular models used in weather forecasting.

Author: Cedric Archambeau, University Of Southampton

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