Introduction to measure theory, Lp spaces and Hilbert spaces. Random variables, expectation, conditional expectation, conditional distribution. Uniform integrability, almost sure and Lp convergence. Stochastic processes: definition, stationarity, sample path continuity. Examples: random walk, Markov chains, Gaussian processes, Poisson processes, Martingales. Construction and basic properties of Brownian motion. Prerequisite: Math MATH 151 or Stats MATH 117, and Math MATH 115 (or equivalent for writing single-variable analysis proofs).
4 units · Letter or Credit/No Credit · GER: WAY-FR
Introduction to measure theory, Lp spaces and Hilbert spaces. Random variables, expectation, conditional expectation, conditional distribution. Uniform integrability, almost sure and Lp convergence. Stochastic processes: definition, stationarity, sample path continuity. Examples: random walk, Markov chains, Gaussian processes, Poisson processes, Martingales. Construction and basic properties of Brownian motion. Prerequisite: Math 151 or Stats 117, and Math 115 (or equivalent for writing single-variable analysis proofs).
Offered in Autumn 2025 at Stanford University.