Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-26T01:12:08.124Z Has data issue: false hasContentIssue false

Unstable invariant distributions for a class of stochastic delay equations

Published online by Cambridge University Press:  20 January 2009

S. E. A. Mohammed
Affiliation:
Mathematics DepartmentSouthern Illinois University at CarbondaleCarbondaleIllinois 62901, U.S.A.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In our article [8] we examined asymptotic mean square stability for linear retarded f.d.e.'s which are perturbed by white noise. It is shown in [8] and [10] that if the deterministic linear retarded f.d.e. is asymptotically stable, then so is the perturbed stochastic f.d.e.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

REFERENCES

1.Bailey, H. R. and Williams, M. Z., Some results on the differential-difference equation , J. Math. Anal. Appl. 15 (1966), 569587.CrossRefGoogle Scholar
2.Chung, K. L., Lectures from Markov processes to Brownian motion (Springer-Verlag, New York-Heidelberg-Berlin, 1982).CrossRefGoogle Scholar
3.Doob, J. L., Stochastic processes (Wiley, New York, 1967).Google Scholar
4.Elworthy, K. D., Stochastic differential equations on manifolds (LMS Lecture Note Series 70, Cambridge University Press, Cambridge, 1982).CrossRefGoogle Scholar
5.Hale, J. K., Theory of functional differential equations (Springer-Verlag, New York-Heidelberg-Berlin, 1977).CrossRefGoogle Scholar
6.Hale, J. K. and Perello, C., The neighborhood of a singular point of functional-differential equations, Cont. Differential Equations 3 (1964), 351375.Google Scholar
7.Lipster, R. S. and Shiryayev, A. N., Statistics of random processes I, General theory (Springer-Verlag, New York-Heidelberg-Berlin, 1977).Google Scholar
8.Mohammed, S. E. A., Stability of linear delay equations under a small noise, Proc. Edinburgh Math. Soc. 29 (1986), 233254.CrossRefGoogle Scholar
9.Mohammed, S. E. A., Stochastic functional differential equations (Research Notes in Mathematics 99, Pitman Advanced Publishing Program, Boston-London-Melbourne, 1984).Google Scholar
10.Mohammed, S. E. A., Scheutzow, M. and Weizsäcker, H. V., Hyperbolic state space decomposition for a linear stochastic delay equation, SIAM J. Control Optim. 24 (1986), 543551.CrossRefGoogle Scholar
11.Stroock, D. W. and Varadhan, S. R. S., Multidimensional diffusion processes (Springer-Verlag, Berlin-Heidelberg-New York, 1979).Google Scholar