Poissonian subordinators, the Wiener–Ornstein–Uhlenbeck field, and a relation between the Ornstein–Uhlenbeck processes and Brownian bridges

Autor:	O. V. Rusakov
Rok vydání:	2011
Předmět:	Statistics and Probability Sequence Applied Mathematics General Mathematics Mathematical analysis Ornstein–Uhlenbeck process Brownian excursion Scaling limit Tensor product Mathematics::Probability Diffusion process Limit (mathematics) Brownian motion Mathematics
Zdroj:	Journal of Mathematical Sciences. 176:232-238
ISSN:	1573-8795 1072-3374
DOI:	10.1007/s10958-011-0414-7
Popis:	We apply to a sequence of i.i.d. random variables a time change operator via a Poisson process that is independent of this sequence. We consider sums of independent copies of processes constructed in this way and having continuous time. Finite limit distributions of these sums coincide with the finite limit distributions of the Wiener–Ornstein–Uhlenbeck field that is the tensor product of a Brownian motion and the Ornstein–Uhlenbeck process. The transition characteristics of the limit Ornstein–Uhlenbeck process are described by Brownian bridges that are builded into the Wiener–Ornstein–Uhlenbeck field. Bibliography: 4 titles.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::711d3ade02f9383b05ee91653dca0bda https://doi.org/10.1007/s10958-011-0414-7 Zobrazit plný text záznamu Plný text ve formátu PDF