Poisson random measures, Lévy processes, generalized stochastic calculus, continuous state branching processes
 发布时间： 2017-10-13     10:22   【返回上一页】 发布人：Etienne Pardoux教授

The Poisson distribution appears very naturally as the law of a random cloud of points, under mild conditions. We will define and study Poisson Random measures of points. We shall then show how to use them in order to define all Lévy processes other than the Brownian motion. This requires defining stochastic integrals of deterministic functions with respect to a compensated Poisson random measure. We shall also integrate predictable random processes, establish a generalized Itô formula, solve SDEs directed by a Lévy process, and prove the Markov property of the solution. Finally we shall study Dawson-Li type SDEs, whose solutions are general continuous state branching processes. We shall see that the Lamperti transform changes those into Lévy processes.

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