Mathematical Finance, Stochastic Analysis, and Machine Learning Seminar by Tomasz Bieleck: On Function of Evolution of Distribution for Time Homogeneous Markov Processes

Speaker: Tomasz Bielecki, Illinois Institute of Technology

Title: On Function of Evolution of Distribution for Time Homogeneous Markov Processes.

Abstract: A study of time homogeneous, real valued Markov processes with a special property and a non-atomic initial distribution is provided. The new notion  of a function of evolution of distribution which determines the dependency between one dimensional distributions of a process is introduced. This, along with the notion of bridge operators which determine the backward structure, as opposed to the forward structure determined by the usual semi-group operators, paves a way to the new  approach for dealing with finite-dimensional distributions of Markov processes. This, in particular, produces explicit formulas which effectively simplify the computations of finite-dimensional distributions,  giving an alternative to the standard approach based on computations using the chain rule of transition densities.

 

Mathematical Finance, Stochastic Analysis, and Machine Learning Seminar