Naslov
Markov chain approximation of pure jump processes

Autori
Mimica, Ante ; Sandrić, Nikola ; Schilling, Rene

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, neobjavljeni rad, znanstveni

Skup
8th International Conference on Lévy Processes

Mjesto i datum
Angers, Francuska, 25.07.2016. - 29.07.2016

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
Non-symmetric Dirichlet form ; Non-symmetric Hunt process ; Markov chain ; Mosco convergence ; Semimartingale ; Semimartingale characteristics ; Weak convergence

Sažetak
Let $\{; ; X^{; ; n}; ; \}; ; _{; ; n\in\mathbb{; ; N}; ; }; ; $ be a sequence of Markov chains on $n^{; ; -1}; ; \mathbb{; ; Z}; ; ^{; ; d}; ; $, and let $X$ be a Markov process on $\R^{; ; d}; ; $. The following two questions naturally arise: \begin{; ; enumerate}; ; \item [1.] When does $\{; ; X^{; ; n}; ; \}; ; _{; ; n\in\mathbb{; ; N}; ; }; ; $ converge weakly to a Markov process? \item [2.] Can $X$ be approximated (in the sense of weak convergence) by a sequence of Markov chains? \end{; ; enumerate}; ; These two problems are very well investigated in the case of diffusion processes and symmetric pure jump Markov processes (generated by a symmetric nonlocal Dirichlet form). In this talk, we focus on a class of pure jump Markov processes generated by: (i) a nonsymmetric nonlocal Dirichlet form or (ii) semimartingale characteristics, and we discuss conditions for weak convergence of a sequence of Markov chains to a process in this class and Markov chain approximation of processes in this class.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA