Bayesian inference for deriving some stochastic process

Abstract

This master's thesis explores Bayesian inference techniques for stochastic processes. Stochastic processes are mathematical models that describe random phenomena evolving over time. Bayesian inference is a statistical approach for estimating unknown model parameters and making predictions based on observed data. The thesis provides an introduction to stochastic processes and Bayesian inference, and then focuses on the application of Bayesian techniques to three specific stochastic processes: the Geometric Brownian motion process, the Multivariate Merton model, and the term structure model. The thesis presents detailed derivations of Bayesian inference methods for these models, and provides numerical examples to illustrate the practical implementation of the methods. The results demonstrate the effectiveness of Bayesian inference for estimating model parameters and making predictions for stochastic processes. The thesis concludes with a discussion of the strengths and limitations of Bayesian inference for stochastic processes, and suggests directions for future research.