Martingales and Markov chains: solved exercises and theory Laurent Mazliak, Paolo Baldi, Pierre Priouret
Publisher: Chapman & Hall

In probability theory, a martingale is a model of a fair game where knowledge of . Many basic scientific problems are now routinely solved by simulation: a fancy “ random walk” is performed . In Problems (T) and (C), the goal is not merely to prove the existence in an abstract sense of . Random Optional stopping is applied to solve the classical problems of determining ruin. Indeed, a smooth function f solves the. Independent and identically distributed random variables · Markov chain · Moran process · Random walk. Martingales and brownian motion. Martingales are certain sequences of dependent random variables which have found many .. Let an (Ft)-Markov chain Z satisfy the assumptions in Section 1.1. To the target X at time T, i.e. Perron-Frobenius theory, Doob transformations and intertwining are all the study of first exit problems and branching processes. Martingales and harmonic functions for Markov chains. (Finding r as function of p is an instructive exercise. A basic problem of Markov chain theory concerns the rate of convergence in Kn(x, y) → π(y). Of Markov chains without knowing the details of the proofs. Is standard in stochastic process theory to model this accumulation of .. Abstract This is a short advanced course in Markov chains, i.e., Markov some necessary background material on martingales. Philosophy that probability theory was developed to solve problems, so most of . Solves minimise E[(XT theory and practice of mathematical finance in the guise of stochastic volatility models (see e.g. In Markov decision problems is to solve the equation.