Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations
Publication
, Journal Article
Bakhtin, Y; Mattingly, JC
Published in: Communications in Contemporary Mathematics
October 1, 2005
We explore Itô stochastic differential equations where the drift term possibly depends on the infinite past. Assuming the existence of a Lyapunov function, we prove the existence of a stationary solution assuming only minimal continuity of the coefficients. Uniqueness of the stationary solution is proven if the dependence on the past decays sufficiently fast. The results of this paper are then applied to stochastically forced dissipative partial differential equations such as the stochastic Navier-Stokes equation and stochastic Ginsburg-Landau equation. © World Scientific Publishing Company.
Duke Scholars
Published In
Communications in Contemporary Mathematics
DOI
ISSN
0219-1997
Publication Date
October 1, 2005
Volume
7
Issue
5
Start / End Page
553 / 582
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4902 Mathematical physics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Bakhtin, Y., & Mattingly, J. C. (2005). Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations. Communications in Contemporary Mathematics, 7(5), 553–582. https://doi.org/10.1142/S0219199705001878
Bakhtin, Y., and J. C. Mattingly. “Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations.” Communications in Contemporary Mathematics 7, no. 5 (October 1, 2005): 553–82. https://doi.org/10.1142/S0219199705001878.
Bakhtin Y, Mattingly JC. Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations. Communications in Contemporary Mathematics. 2005 Oct 1;7(5):553–82.
Bakhtin, Y., and J. C. Mattingly. “Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations.” Communications in Contemporary Mathematics, vol. 7, no. 5, Oct. 2005, pp. 553–82. Scopus, doi:10.1142/S0219199705001878.
Bakhtin Y, Mattingly JC. Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations. Communications in Contemporary Mathematics. 2005 Oct 1;7(5):553–582.
Published In
Communications in Contemporary Mathematics
DOI
ISSN
0219-1997
Publication Date
October 1, 2005
Volume
7
Issue
5
Start / End Page
553 / 582
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4902 Mathematical physics
- 0101 Pure Mathematics