Abstract
Abstract This chapter reviews the theory of continuous-time stochastic processes, covering the concepts of adaptation, Lévy processes, diffusions, martingales, and Markov processes. Brownian motion is studied as the most important case, with properties that include the reflection principle and the strong Markov property. The technique of Skorokhod embedding is introduced, providing novel proofs of the central limit theorem and the law of the iterated logarithm. The family of processes derived from Brownian motion is reviewed and in the final section it is shown that a continuous process having finite variance and independent increments is Brownian motion.
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