Universität zu Köln

Bailleul, I., Riedel, S. and Scheutzow, M. (2017). Random dynamical systems, rough paths and rough flows. J. Differ. Equ., 262 (12). S. 5792 - 5824. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE. ISSN 1090-2732

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Abstract

We analyze common lifts of stochastic processes to rough paths/rough drivers-valued processes and give sufficient conditions for the cocycle property to hold for these lifts. We show that random rough differential equations driven by such lifts induce random dynamical systems. In particular, our results imply that rough differential equations driven by the lift of fractional Brownian motion in the sense of Friz-Victoir [26] induce random dynamical systems. (C) 2017 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Bailleul, I. UNSPECIFIED UNSPECIFIED UNSPECIFIED Riedel, S. UNSPECIFIED UNSPECIFIED UNSPECIFIED Scheutzow, M. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-227710
DOI:	10.1016/j.jde.2017.02.014
Journal or Publication Title:	J. Differ. Equ.
Volume:	262
Number:	12
Page Range:	S. 5792 - 5824
Date:	2017
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE
Place of Publication:	SAN DIEGO
ISSN:	1090-2732
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language DIFFERENTIAL-EQUATIONS DRIVEN; HYPOELLIPTIC SDES DRIVEN; BROWNIAN MOTIONS; WIENER-PROCESSES; ERGODICITY; ATTRACTORS; DIMENSION Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/22771