Title: Martingales and a generalization
Speaker: Christian Gromoll (Associate Professor, University of Virginia)
Abstract: One of the fundamental objects in probability theory is the martingale, which together with its siblings the submartingale and supermartingale can be thought of as a random analogue of the familiar monotone sequence of numbers (constant, nondecreasing, nonincreasing). Just as monotone sequences regularly provide a needed proof ingredient in deterministic settings, martingales provide the same in random settings. In this talk I’ll review some of the most important properties and uses of martingales, and then introduce an interesting generalization of the concept, in which the random sequence “remembers its past.” A variety of martingale-like properties can be shown for this generalization.