|Flow||M - Mathematics|
|Category||Obligatory by selection|
|Class Hours - Lab Hours||4 - 0|
|Lecturers||Michail Loulakis (School of AMPS),|
Construction and description of Stochastic Processes, finite dimensional distributions. Markov Chains, transition probabilities, Chapman-Kolmogorov equations, communication classes. Stopping times, strong Markov property, recurrence and transience. Potential Theory: boundary value problems for absorption probabilities, mean hitting times. Random walks. Invariant distributions, existence, uniqueness, time reversibility, detailed balance. Coupling, period, convergence to equilibrium, renewal theorem, ergodic theorem. Mixing time and relaxation time. Applications: Web search, electrical networks and Rayleigh’s principle, Metropolis-Hastings algorithm, Ising model, Simulated annealing. Poisson processes: independence of increments, thinning and summation. Compound Poisson processes. The course in accompanied by a virtual lab in Python.