Theoretical Statistics and Mathematics Unit, ISI Delhi

December 5, 2018 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Umesh Kumar,
Rajdhani College, University of Delhi

Title:
The Stochastic Cauchy Problem Driven by a Cylindrical Levy Process

Abstract of Talk

A cylindrical L´evy process is a generalisation of a cylindricalWeiner process and is defined using cylindrical measures and cylindrical random variables. The theory of integration of deterministic functions with respect to a cylindrical L´evy process was recently introduced and can be used to study the stochastic Cauchy problem. In this talk, we prove the existence and uniqueness of solution of a stochastic Cauchy problem driven by a cylindrical L´evy process. Our approach requires to first prove a stochastic version of the Fubini theorem. The solution process is stochastically continuous, satisfies Markov property and has scalarly square integrable paths. We will also discuss the necessary and sufficient conditions for the existence of invariant measure for the solution process.
(Joint work with Markus Riedle, King’s College London)