Abstract
In this chapter the strong Markov property is derived as an extension of the Markov property to certain random times, called stopping times. A number of consequences of the strong Markov property of Brownian motion and the simple random walk are derived. A derivation of the law of the iterated logarithm for Brownian motion is included in this chapter, from which some fine scale sample path properties of Brownian motion are derived as well.
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