Continuity in a pathwise sense with respect to the coefficients of solutions of stochastic differential equations

Thomas Skov Knudsen

Stochastic Processes and their Applications, 1997, vol. 68, issue 2, 155-179

Abstract: For stochastic differential equations (SDEs) of the form dX(t) = b(X)(t)) dt + [sigma] (X(t))dW(t) where b and [sigma] are Lipschitz continuous, it is shown that if we consider a fixed [sigma] [epsilon] C5, bounded and with bounded derivatives, the random field of solutions is pathwise locally Lipschitz continuous with respect to b when the space of drift coefficients is the set of Lipschitz continuous functions of sublinear growth endowed with the sup-norm. Furthermore, it is shown that this result does not hold if we interchange the role of b and [sigma]. However for SDEs where the coefficient vector fields commute suitably we show continuity with respect to the sup-norm on the coefficients and a number of their derivatives.

Keywords: 60H10 (search for similar items in EconPapers)
Date: 1997
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(97)00024-0
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:68:y:1997:i:2:p:155-179

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 ().