Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

Itô and Stratonovich stochastic partial differential equations: Transition from microscopic to macroscopic equations


Author: Peter M. Kotelenez
Journal: Quart. Appl. Math. 66 (2008), 539-564
MSC (2000): Primary 60H10, 60H05, 60H30, 60F17
Published electronically: July 2, 2008
MathSciNet review: 2445528
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract:

We review the derivation of stochastic ordinary and quasi-linear stochastic partial differential equations (SODE's and SPDE's) from systems of microscopic deterministic equations in space dimension $ d\geq 2$ as well as the macroscopic limits of the SPDE's. The macroscopic limits are quasi-linear (deterministic) PDE's. Both noncoercive and coercive SPDE's, driven by Itô differentials with respect to correlated Brownian motions, are considered. For the solutions of semi-linear noncoercive SPDE's with smooth and homogeneous diffusion kernels we show that these solutions can be obtained as solutions of first-order SPDE's, driven by Stratonovich differentials and their macroscopic limit, and are solutions of a class of semi-linear second-order parabolic PDE's. Further, the space-time covariance structure of correlated Brownian motions is described and for space dimension $ d\geq 2$ the long-time behavior of the separation of two uncorrelated Brownian motions is shown to be similar to the independent case.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 60H10, 60H05, 60H30, 60F17

Retrieve articles in all journals with MSC (2000): 60H10, 60H05, 60H30, 60F17


Additional Information

Peter M. Kotelenez
Affiliation: Department of Mathematics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106
Email: pxk4@po.cwru.edu

DOI: http://dx.doi.org/10.1090/S0033-569X-08-01102-6
PII: S 0033-569X(08)01102-6
Received by editor(s): May 15, 2007
Published electronically: July 2, 2008
Article copyright: © Copyright 2008 Brown University
The copyright for this article reverts to public domain 28 years after publication.



Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2015 Brown University
Comments: qam-query@ams.org
AMS Website