ABSTRACT
We now develop likelihood methods for inference about parameters that determine the drift andjump mechanism of adiffusion process with jumps fol- lowing Sorensen [24, 25]. We assume that a continuously observed sample path is available. There are various situations where stochastic modeling through diffusion with jumps is found to be appropriate. Applications of such models include general stock price model in [1, 2], modeling soil moisture [21], hydrol- ogy [6], etc. The theory we will discuss here generalizes results for ordinary diffusions discussed in [4] and [19]. An extensive discussion is given in [22] on parametric as well as nonparametric inference for diffusion type processes with methods and applications, in both the cases when complete realizations of the sample paths of the process are available in the ideal case as well as when sampled data of the process is available. We will not go into these aspects here. A typical example of a difsion with jumps is the solution of the stochastic differential equation
