2022/06/19 by Tomasz R. Bielecki, Bielecki, Tomasz, Jacek Jakubowski +3
Business, Management and Accounting · Computer Science · Decision Sciences · #60H30 #60J35 #91G80 #Advanced Queuing Theory Analysis #FOS: Mathematics #Petri Nets in System Modeling #Probability (math.PR) #Simulation Techniques and Applications
paper · pdf · doi:10.48550/arxiv.2206.09451
openalex publication_date 2022/06/19 · openalex created_date 2022/06/24 · openalex updated_date 2026/07/28
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. Various examples illustrating the new approach are presented.