Non-exponential stability of scalar stochastic Volterra equations

Statistics and Probability Letters

Volumn 62, Issue 4, 2003, Pages 335-343

  Appleby, John A D ^a   Reynolds, David W ^a  

^a DUBLIN CITY UNIVERSITY   (Ireland)

Author keywords

Almost sure exponential asymptotic stability; It Volterra equations; Stochastic integrodifferential equations

Indexed keywords

EID: 0037404217     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-7152(03)00035-X     Document Type: Article

References (18)

1. Appleby J.A.D. Reynolds D.W. On the non-exponential convergence of asymptotically stable solutions of linear scalar Volterra integro-differential equations J. Integral Equations Appl. 14 2 2002 109 118
2. Appleby J.A.D. Reynolds D.W. Subexponential solutions of linear Volterra integro-differential equations and transient renewal equations Proc. Roy. Soc. Edinburgh. Sect. A 132 1 2002 521 543
3. Berger M.A. Mizel V.J. Volterra equations with Itô integrals I J. Integral Equations 2 3 1980 187 245
4. Karatzas I. Shreve S.E. Brownian Motion and Stochastic Calculus 1991 Springer New York
5. Liu K. Some remarks on exponential stability of stochastic differential equations Stochastic Anal. Appl. 19 1 2001 59 65
6. Liu K. Mao X. Exponential stability of non-linear stochastic evolution equations Stochastic Process. Appl. 78 1998 173 193
7. Liu K. Mao X. Large time behaviour of dynamical equations with random perturbation features Stochastic Anal. Appl. 19 2 2001 295 327
8. Mao X. Exponential stability in mean-square for stochastic differential equations Stochastic Anal. Appl. 8 1 1990 91 103
9. Mao X. Almost sure polynomial stability for a class of stochastic differential equations Quart. J. Math. Oxford Ser. (2) 43 2 1992 339 348
10. Mao X. Polynomial stability for perturbed stochastic differential equations with respect to semimartingales Stochastic Process. Appl. 41 1992 101 116
11. Mao X. Stochastic stabilization and destabilization Systems Control Lett. 23 1994 279 290
12. Mao X. Exponential Stability of Stochastic Differential Equations 1994 Marcel Dekker New York
13. Mao X. Stochastic Differential Equations and Applications 1997 Horwood Chichester
14. Mao X. Stability of stochastic integro-differential equations Stochastic Anal. Appl. 18 6 2000 1005 1017
15. Mao X. Shah A. Exponential stability of stochastic delay differential equations Stochastics Stochastics Rep. 60 1 1997 135 153
16. Mizel V.J. Trutzer V. Stochastic heredity equations: existence and asymptotic stability J. Integral Equations 7 1984 1 72
17. Mohammed S.-E.A. Scheutzow M.K.R. Lyapunov exponents of linear stochastic functional-differential equations. II. Examples and case studies Ann. Probab. 25 3 1997 1210 1240
18. Murakami S. Exponential asymptotic stability of scalar linear Volterra equations Differential Integral Equations 4 3 1991 519 525