seminar: Relation between stochastic integrals w.r.t. Levy processes, compensated Poisson random measures, and the geometry of Banach spaces
speaker: Barbara Rüdiger (Mathematisches Institut , Universität Koblenz -Landau, Campus Koblenz)abstract: n the literature stochastic differential equations with Lévy noise have been introduced either by analyzing stochastic integrals w.r.t. Levy processes or w.r.t. compensated Poisson random measures (cPrm). Moreover different definitions of stochastic integrals w.r.t. cPrm have been introduced. In this talk we report some work where the different definitions of stochastic integral are compared. In fact all these different notions of stochastic integrals can be unified, by remarking that the definition of Ito integral w.r.t. cPrm is stronger. We report such results also on separable Banach spaces of M -type 2 or type 2. We also answer to the following natural questions: When is the M -type 2 (resp. type 2) condition necessary for the existence of the Ito integral w.r.t. cPrm? By introducing Pettis integrals w.r.t. cPrm, may we skip the M -type 2 (resp. type 2) condition?
AR S. Albeverio, B. Rüdiger, The Lévy -Ito decomposition theorem and stochastic integrals, on separable Banach spaces, Stoch. An. and Appl. (2004).
MR V. Mandrekar, B. Rüdiger, Stochastic integrals w.r.t. compensated Poisson random measures and the geometry of Banach spaces, manuscript
MR2 V. Mandrekar, B. Rüdiger, Existence and uniqueness of path wise solutions for stochastic integral equations driven by non Gaussian noise on separable Banach spaces, submitted
MR3 V. Mandrekar, B. R Rüdiger, Lévy noises and stochastic integrals on Banach spaces, to appear on "Stochastic Partial Differential Equations and Applications - VII", Lecture Notes in Pure and Applied Mathematics, CRC Press (2005).
Ru Rüdiger, Stochastic integration with respect to compensated Poisson random measures on separable Banach spaces, Stoch. Stoch. Rep., 213 -242, {Vol. 76}, No. 3, (June 20004).
timetable:
Wed 5 Apr, 16:30 - 17:10, Aula Dini
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