Likelihood Methods for Diffusions with Jumps

Abstract

Likelihood methods are developed for inference about parameters that determine the drift and the jump mechanism of a diffusion with jumps. The data are supposed to be a continuously observed sample path. The powerful tools of stochastic calculus are finding their way into many branches of applied probability and statistics these years. These methods have enabled analysis of more complicated models than could be handled earlier. This chapter investigates likelihood methods for inference about parameters that determine the drift coefficient and the jump mechanism. It reviews the mathematics of diffusions with jumps, and the type of models considered in the paper is defined. The chapter demonstrates how the theory simplifies and can be sharpened when a part of the likelihood function has the form of an exponential family. It also illustrates various aspects of the theory.

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