Gaussian Processes and Brownian Motion

Abstract

Covariance and independence, rotational symmetry, isonormal Gaussian process, independent increments, Brownian motion and bridge, scaling and inversion, Gaussian Markov processes, quadratic variation, path irregularity, strong Markov and reflection properties, Bessel processes, maximum process, arcsine and uniform laws, laws of the iterated logarithm, Wiener integral, spectral and moving-average representations, Ornstein–Uhlenbeck process, multiple Wiener–Itô integrals, chaos expansion of variables and processes.