The parametrix method approach to diffusions in a turbulent Gaussian environment

Tomasz Komorowski

Stochastic Processes and their Applications, 1998, vol. 74, issue 2, 165-193

Abstract: In this paper we deal with the solutions of Itô stochastic differential equationfor a small parameter [epsilon]. We prove that for 0[less-than-or-equals, slant][alpha] 0 converges weakly to a Brownian motion. The entries of the covariance matrix of the limiting Brownian motion are given by ai,j=2[delta]i,j+[integral operator]+[infinity]-[infinity]Ri,j(t,0)Â dt, i,j=1,...,d, where [Ri,j(t,x)] is the covariance matrix of the field V. To obtain this result we apply a version of the parametrix method for a linear parabolic PDE (see Friedman, 1963).

Keywords: Random; Guassian; field; Mixing; condition; Weak; convergence; of; stochastic; processes (search for similar items in EconPapers)
Date: 1998
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(97)00122-1
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:74:y:1998:i:2:p:165-193

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().