Probability Theory and Stochastic Processes (Paperback, 2020)

IIntroduction.-Warming Up.- Integration Theory for Probability.- Probability and Expectation.- Convergence of random sequences.- Markov Chains.- Martingale Sequences.- Ergodic Sequences.- Generalities on Stochastic Processes.- Poisson Processes.- Continuous-Time Markov Chains.- Renewal Theory in Continuous Time.- Brownian Motion.- Wide-sense Stationary Stochastic Processes.- An Introduction to Ito’s Calculus.- Appenndix: Number Theory and Linear Algebra.- Analysis.- Hilbert Spaces.- Z-Transforms.- Proof of Paul Levy’s Criterion.- Direct Riemann Integrability.- Bibliography.- Index.