Exploring Markov properties and their consequences through mathematical proofs and illustrations.
R · Stochastic processes
For this seminar project in applied probability, I prepared a paper and presentation on the Markov properties of Brownian motion, drawing on Brownian Motion by Mörters and Peres. I presented definitions and proofs, explained how the strong Markov property extends from fixed times to stopping times, and derived Blumenthal’s zero-one law and the reflection principle as consequences of the Markov properties. Examples, counterexamples and simulated paths created in R complement the mathematical arguments and illustrate the distinctions between the properties.