Approximate Likelihood Construction for Rough Differential Equations

Abstract

The paper is split in two parts: in the first part, we construct the exact likelihood for a discretely observed rough differential equation, driven by a piecewise linear path. In the second part, we use this likelihood in order to construct an approximation of the likelihood for a discretely observed differential equation driven by a general class of rough paths. Finally, we study the behaviour of the approximate likelihood when the sampling frequency tends to infinity.

References in corpus (3)

• Learning from the past, predicting the statistics for the future, learning an evolving system
• A Levy-area between Brownian motion and rough paths with applications to robust non-linear filtering and RPDEs
• Statistical Inference for Stochastic Differential Equations with Memory