Comparison of the long-time behavior of linearito and stratonovich partial differential equations

Stochastic Analysis and Applications

Volumn 19, Issue 2, 2001, Pages 183-195

  Caraballo, Tomás ^a   Langa, José A ^a  

^a UNIVERSITY OF SEVILLE   (Spain)

Author keywords

Almost sure exponential stability; Destabilization; Linear ito PDE; Linear Stratonovich PDE; Stabilization

Indexed keywords

EID: 0035531448     PISSN: 07362994     EISSN: None     Source Type: Journal    
DOI: 10.1081/SAP-100000758     Document Type: Article

References (11)

1. Arnold, L. Stochastic Differential Equations: Theory and Applications; Wiley & Sons: New York, 1974.
2. Oksendal, B. Stochastic Differential Equations; Springer-Verlag: Berlin, 1992.
3. Kunita, H. Stochastic Partial Differential Equations Connected with Non-Linear Filtering. In Lecture Notes in Mathematics; S.K. Mitter and A. Moro, Eds.; Springer Berlin 1982; Vol. 972, 100-169.
4. Datko, R. Extending a Theorem of A.M. Lyapunov to Hilbert Space. J. Math. Anal. Appl. 1970, 32, 610-616.
5. Da Prato, G.; Zabczyk, J. Stochastic Equations in Infinite Dimensions; Cambridge University Press: Cambridge, England, 1992.
6. Pazy, A. Semigroups of Linear Operators and Applications to Partial Differential Equations; Springer-Verlag: New York, 1983.
7. Arnold, L. Stabilization by Noise Revisited. Z. Angew. Math. Mech. 1990, 70, 235-246.
8. Curtain, R.F.; Pritchard, A.J. Functional Analysis in Modern Applied Mathematics; Mathematics in Science and Engineering Vol. 132 Academic Press: London, 1977.
9. Haus smann, U.G. Asymptotic Stability of the Linear Ito Equation in Infinite Dimensions. J. Math. Anal. Appl. 1978, 65, 219-235.
10. Ichikawa, A. Stability of Semilinear Stochastic Evolution Equations. J. Math. Anal. Appl. 1982, 90, 12-44.
11. Kwiecinska, A.A. Stabilization of Partial Differential Equations by Noise. Stochastic Processes and Their Applications 1999, 79, 179-184.