Keywords
- Lyapunov Exponent
- Invariant Measure
- Stochastic Differential Equation
- Ergodic Property
- Strong Maximum Principle
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
L. Arnold and W. Kliemann (1983). Qualitative theory of stochastic systems. In Probabilistic Analysis and Related Topics (A. T. Bharucha-Reid, ed.) 3 1–79. Academic Press, New York.
L. Arnold, E. Oeljeklaus and E. Pardoux (1986). Almost sure and moment stability for linear Itô equations. In Lyapunov exponents (L. Arnold, V. Wihstutz, eds) Lect. Notes Math. 1186 129–159. Springer, Berlin Heidelberg New York.
R. Azencott (1974). Behavior of diffusion semi-groups at infinity. Bull. Soc. Math. France 102 193–240.
P. H. Baxendale (1987). Moment stability and large deviations for linear stochastic differential equations. In Proc. Taniguchi Symposium on Probabilistic Methods in Mathematical Physics. Katata and Kyoto 1985. (N. Ikeda, ed.) 31–54. Kinokuniya, Tokyo.
P. H. Baxendale (1990). Statistical equilibrium and two-point motion for a stochastic flow of diffeomorphisms. In Spatial Stochastic Processes: Festschrift for T. E. Harris (K. Alexander, J. Watkins, eds) Birkhauser, Boston Basel Stuttgart (in press).
P. H. Baxendale and D. W. Stroock (1988). Large deviations and stochastic flows of diffeomorphisms. Probab. Th. Rel. Fields 80 169–215.
R. N. Bhattacharya (1978). Criteria for recurrence and existence of invariant measures for multidimensional diffusions. Ann. Probab. 6 541–553.
A. P. Carverhill (1985). Flows of stochastic dynamical systems: ergodic theory. Stochastics 14 273–317.
A. Friedman (1973). Wandering out to infinity of diffusion processes. Trans. Am. Math. Soc. 184 185–203.
R. Z. Khas'minskii (1960). Ergodic properties of recurrent diffusion processes and stabilization of the solution of the Cauchy problem for parabolic equations. Theory Probab. Appl. 5 179–196.
R. Z. Khas'minskii (1967). Necessary and sufficient conditions for the asymptotic stability of linear stochastic systems. Theory Probab. Appl. 12 144–147.
R. Z. Khas'minskii (1980). Stochastic stability of differential equations. Sijthoff and Noordhoff, Alphen aan den Rijn.
W. Kliemann (1987). Recurrence and invariant measures for degenerate diffusions. Ann. Probab. 15 690–707.
G. Maruyama and H. Tanaka (1959). Ergodic property of N-dimensional recurrent Markov processes. Mem. Fac. Sci. Kyushu Univ. A-13 157–172.
V. I. Oseledec (1968). A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems. Trans. Moscow Math. Soc. 19 197–231.
D. Ruelle (1979). Ergodic theory of differential dynamical systems. Publ. Math. IHES 50 275–306.
D. W. Stroock (1986). On the rate at which a homogeneous diffusion approaches a limit, an application of the large deviation theory of certain stochastic integrals. Ann. Probab. 14 840–859.
D. W. Stroock and S. R. S. Varadhan (1972). On the support of diffusion processes with applications to the strong maximum principle. Proc. Sixth Berkeley Symp. Math. Statist. Probab. 3 333–359. Univ. California Press.
D. W. Stroock and S. R. S. Varadhan (1979). Multidimensional diffusion processes. Springer, Berlin Heidelberg New York.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag
About this paper
Cite this paper
Baxendale, P.H. (1991). Invariant measures for nonlinear stochastic differential equations. In: Arnold, L., Crauel, H., Eckmann, JP. (eds) Lyapunov Exponents. Lecture Notes in Mathematics, vol 1486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086663
Download citation
DOI: https://doi.org/10.1007/BFb0086663
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54662-7
Online ISBN: 978-3-540-46431-0
eBook Packages: Springer Book Archive
