MATE-3510 Stochastic Processes

Introduction. Stochastic processes specifications. Some important classes of processes such as stationary processes. Processes with stationary increments and processes with independent increments. Markov processes. Martingales. MARKOV CHAINS: definitions and examples. Features. Finite Markov chains. Classification of states and chains. Markov chains accounting. Limit theorems. Stationary distribution. POISSON PROCESSES: generalizations of Poisson processes. not homogeneous process. Compound Poisson processes. Conditional processes. Processes of birth and death. MARTINGALA in discrete time: conditional expected value. Definition and examples. Time to Stop. Optional stopping theorem. Inequalities of the Doob Martingale. Convergence Theorem of Martingala. RENEWAL PROCESSES : Renewal Equation. Laws of large numbers. Age and residual life. Applications to the theory of the tail. Brownian motion: Preliminaries. Simple Features of standard Brownian motion. Variations in the Brownian motion. Brownian motion with drift. Kolomogorov equations. Ornstein-Uhlenbeck process.




Arunachalam Viswanatham