The Predictable Compensator Of The Piecewise Diffusion Process And Some Properties

In this paper, we mainly studies the predictable compensator of the piecewise diffusion process and some properties.The compound Poisson model with diffusion, firstly proposed by Ger-ber in 1970, is the further expansion of the compound Poisson model. Developing the compound Poisson model further with considering the models in finance, we get piecewise diffusion process. First of all, we propose the definition of the piecewise diffusion process. Then, we obtain some expectation and condition expectation of some random variables. After that, we compute the predictable compensator of the random measure. Moreover, we get Ito formulation of the piecewise diffusion process.This paper includes four chapters. The first chapter is the introduction. In the second chapter, the definition of the piecewise diffusion process is proposed. Furthermore, we introduce the definition of the Stieltjes version of exponentials and logarithms. Some expectation and condition expectation is calculated in the third chapter-the main body of this paper. Moreover, we get the predictable compensator of the random measure. Then, the version of the Ito formulation is shown. The last chapter gives a conclusion.