ABSTRACT
Bayesian inferential methods of estimation, testing hypotheses, and forecasting will reveal interesting aspects of stochastic processes that are unique. This chapter begins with the Brownian motion process, which is a normal process first used to describe the motion of tiny particles in a solution. It presents Bayesian inferences for the parameters of Brownian motion with drift parameters. The chapter also presents comments on the content presented for making Bayesian inferences about stochastic processes that are continuous in state and time. It describes two variations of Brownian motion: the geometric Brownian motion and the Brownian bridge motion along with applications that demonstrate the versatility of the process. Bayesian inferences are especially interesting when applied to examples from finance such as stock options and derivatives. Martingales offer more complex stochastic processes that are a challenge to the Bayesian. The chapter concludes with the broad subject of martingales which is a generalization of normal processes, including the Brownian motion.
