Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Flows associated to Cameron-Martin type vector fields on path spaces over a Riemannian manifold

Flows associated to Cameron-Martin type vector fields on path spaces over a Riemannian manifold The flow on the Wiener space associated to a tangent process constructed by Cipriano and Cruzeiro, as well as by Gong and Zhang does not allow to recover Driver’s Cameron-Martin theorem on Riemannian path space. The purpose of this work is to refine the method of the modified Picard iteration used in the previous work by Gong and Zhang and to try to recapture and extend the result of Driver. In this paper, we establish the existence and uniqueness of a flow associated to a Cameron-Martin type vector field on the path space over a Riemannian manifold. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Flows associated to Cameron-Martin type vector fields on path spaces over a Riemannian manifold

Acta Mathematicae Applicatae Sinica , Volume 29 (3) – Nov 20, 2013

Loading next page...
 
/lp/springer-journals/flows-associated-to-cameron-martin-type-vector-fields-on-path-spaces-Rv4AgLPMQN
Publisher
Springer Journals
Copyright
Copyright © 2013 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-013-0245-z
Publisher site
See Article on Publisher Site

Abstract

The flow on the Wiener space associated to a tangent process constructed by Cipriano and Cruzeiro, as well as by Gong and Zhang does not allow to recover Driver’s Cameron-Martin theorem on Riemannian path space. The purpose of this work is to refine the method of the modified Picard iteration used in the previous work by Gong and Zhang and to try to recapture and extend the result of Driver. In this paper, we establish the existence and uniqueness of a flow associated to a Cameron-Martin type vector field on the path space over a Riemannian manifold.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Nov 20, 2013

References