This is the page of the United Seminar of the Department of Probability Theory of the Faculty of Mechanics and Mathematics of Moscow State University. The permanent website of the seminar is here. The seminar is a continuation of the research seminar of the Department of Probability Theory under the leadership of A.N. Kolmogorov and B.V. Gnedenko.

Upcoming reports

February 11, 16:45 msk

Igor Pavlov, Lomonosov MSU, Russia

Haar Filtrations, Martingale Spaces, and Interpolation of Financial Markets

The brief introduction examines a problem in stochastic analysis identified by A.N. Shiryaev, which led the author of this paper to two research directions. The first direction is the study of the properties of martingale spaces close to L_1 or to L_∞. For martingale spaces L_p̄ with mixed norms (where the components of an infinite-dimensional vector p̄ tend to 1), a generalization of Pelczynski's well-known theorem on the absence of an unconditional basis in this space will be given. A partial solution to Professor E.M. Semenov's problem on the coincidence of L_p̄ with L_∞ will also be presented. The second direction will present results on the interpolation of arbitrage financial markets. It will be shown how this technique is related to Haar interpolation of signed martingale measures. The talk will present the author's results from his two years at MSU.