Almost sure exponential stability for stochastic partial functional differential equations

Stochastic Analysis and Applications

Volumn 16, Issue 5, 1998, Pages 965-975

  Taniguchi, Takeshi ^a  

^a KURUME UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032362535     PISSN: 07362994     EISSN: None     Source Type: Journal    
DOI: 10.1080/07362999808809573     Document Type: Article

References (18)

1. T. Caraballo, Asymptotic exponential stability of stochastic partial differential equations with delay, Stochastic and Stochastics Reports, 33(1990), 27-47.
2. T. Caraballo and J. Real, Partial differential equations with delayed random perturbations: existence, uniqueness, and stability of solutions. Stochastic Analysis and Applications, 11(1993), 497-511.
3. T. Caraballo and J. Real, On the pathwise exponential stability of non-linear stochastic partial differential equations. Stochastic Analysis and Applications, 12(1994), 517-525.
4. P.L. Chow, Stability of nonlinear stochastic evolution equations, Jour. Math. Ana. Appl., 89(1982), 400-419.
5. P.L. Chow and J.L. Menaldi, Exponential estimates in exit probability for some diffusion process in Hilbert spaces, Stochastic and Stochastics Reports, 29(1990), 377-393.
6. R.F. Curtain, Stability of stochastic partial differential equations, Jour. Math. Ana. Appl., 79(1981), 352-369
7. R.F. Curtain and A.J Pritchard, "Infinite Dimensional Linear System Theory", Lect. Notes In Control and Information Sciences, Springer-Verlarg, New York and Berlin, 8(1978).
8. G. DaPrato and J. Zabczyk, "Stochastic Equations in Infinite Dimensions", Cambridge, 1992.
9. G. DaPrato and J. Zabczyk, A note on semilinear stochastic equations, Differential and Integral Equations, 1(1988), 143-155.
10. G. DaPrato and J. Zabczyk, A note on stochastic convolution, Stochastic Analysis and Applications, 10(1992), 143-153.
11. T. Funaki, Random motion of string and related stochastic evolution equations, Nagoya Math. J., 89(1983), 129-193.
12. U.G. Haussmann, Asymptotic stability of the linear Ito equation in infinite dimensions, Jour. Math. Ana. Appl., 64(1978). 219-235.
13. E. Pardoux, Stochastic partial differential equations and filtaring of diffusion process, Stochastics, 3(1979), 127-167.
14. T. Taniguchi, On the estimate of solutions of perturbed linear differential equations, Jour. Math. Anal. Appl., 153(1990), 288-300.
15. T. Taniguchi, Asymptotic stability theorems of semilinear stochastic evolution equations in Hilbert spaces, Stochastics and Stochastics Reports, 53(1995), 41-52.
16. T. Taniguchi, Moment asymptotic behavior and almost sure Lyapunov exponent of stochastic functional differential equations with finite delays via Lyapunov-Razumikhin method, Stochastics and Stochastics Reports. 58(1996), 191-208.
17. C.C. Travis and G.F. Webb. Existence and stability for partial functional differential equations. Trans. A.M.S., 200(1974), 395-418
18. L. Tubaro, An estimate of Burkholder type for stochastic processes defined by the stochastic integral, Stochastic Analysis and Applications, 2(1984), 187-192.