Keywords
- Brownian Motion
- Lyapunov Exponent
- Invariant Measure
- Stochastic Differential Equation
- Iterate Function System
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.
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References
L.M. Abramov and V.A. Rohlin, The entropy of a skew product of measure-preserving transformations, Amer. Math. Soc. Transl. Ser. 2, 48 (1966) 255–265
L. Arnold and P. Boxler, Stochastic bifurcation: Instructive examples in dimension one, in Stochastic Flows, M. Pinsky and V. Wihstutz (eds.). Birkhäuser, Bosten 1991
L. Arnold and H. Crauel, Iterated function systems and multiplicative ergodic theory, in Stochastic Flows, M. Pinsky and V. Wihstutz (eds.). Birkhäuser, Bosten 1991
L. Arnold and W. Kliemann, Large deviations of linear stochastic differential equations, pp. 117–151 in Stochastic Differential Systems, H.J. Engelbert and W. Schmidt (eds.), Lecture Notes in Control and Information Sciences 96. Springer, Berlin 1987
L. Arnold and W. Kliemann, On unique ergodicity for degenerate diffusions, Stochastics 21 (1987) 41–61
L. Arnold, W. Kliemann, and E. Oeljeklaus, pp. 85–125 in Lyapunov Exponents. Proceedings. Bremen 1984, L. Arnold and V. Wihstutz (eds.), Lecture Notes in Mathematics 1186. Springer, Berlin 1986
L. Arnold, E. Oeljeklaus, and E. Pardoux, Almost sure and moment stability for linear Itô equations, pp. 129–159 in Lyapunov Exponents. Proceedings. Bremen 1984, L. Arnold and V. Wihstutz (eds.), Lecture Notes in Mathematics 1186, Springer, Berlin 1986
L. Arnold and V. Wihstutz, pp. 1–26 in Lyapunov Exponents. Proceedings. Bremen 1984, L. Arnold and V. Wihstutz (eds.), Lecture Notes in Mathematics 1186 Springer, Berlin 1986
L. Arnold and Xu Kedai, Normal forms for random dynamical systems, Preprint, Bremen 1991
P. Baxendale, Brownian motions in the diffeomorphism group I, Compositio Mathematica 53 (1984) 19–50
P. Baxendale, Moment stability and large deviations for linear stochastic differential equations, pp. 31–54 in Proceedings of the Taneguchi Symposium on Probabilistic Methods in Mathematics, N. Ikeda (ed.), Katata & Kyoto 1985
M. Bismut, A generalized formula of Itô and some other properties of stochastic flows, Z. Wahrscheinlichkeitstheorie Verw. Geb. 55 (1981) 331–350
T. Bogenschütz, Entropy, pressure and a variational principle for random dynamical systems, Preprint, Bremen 1991
P. Bougerol, Comparaison des exposants de Lyapounov des processus markoviens multiplicatifs, Ann. Inst. Henri Poincaré 24 (1988) 439–489
P. Bougerol, Théorèmes limites pour les systèmes linéaires à coefficients markoviens, Probab. Th. Rel. Fields 78 (1988) 193–221
P. Boxler, A stochastic version of center manifold theory, Probab. Th. Rel. Fields 83 (1989) 509–545
P. Boxler, A necessary condition for a stochastic bifurcation, Preprint, Bremen 1990
R. Carmona and J. Lacroix, Spectral Theory of Random Schrödinger Operators, Birkhäuser, Boston 1990
A. Carverhill, Flows of stochastic dynamical systems: ergodic theory, Stochastics 14 (1985) 273–317
H. Crauel, Extremal exponents of random dynamical systems do not vanish, J. Dynamics Differential Equations 2 (1990) 245–291
H. Crauel, Markov measures for random dynamical systems, Preprint, Bremen 1989
H. Crauel, Non-Markovian invariant measures are hyperbolic, Preprint, Bremen 1990
S. Dahlke, Invariante Mannigfaltigkeiten für Produkte zufälliger Diffeomorphismen, Dissertation, Universität Bremen 1989
K.D. Elworthy, Stochastic dynamical systems and their flows, pp. 79–95 in Stochastic Analysis, A. Friedman and M. Pinsky (eds.). Academic Press 1978
N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes. North Holland-Kodansha, Tokyo 1981
Yu. Kifer, Ergodic Theory of Random Transformations, Birkhäuser, Boston 1986
Yu. Kifer, Characteristic exponents for random homeomorphisms of metric spaces, pp. 74–84 in Lyapunov Exponents. Proceedings. Bremen 1984, L. Arnold and V. Wihstutz (eds.), Lecture Notes in Mathematics 1186, Springer, Berlin 1986
Yu. Kifer, A note on integrability of C r-norms of stochastic flows and applications, pp. 125–131 in Stochastic Mechanics and Stochastic Processes, Proceedings Swansea 1986, Lecture Notes in Mathematics 1325, Springer, Berlin 1988
J.F.C. Kingman, The ergodic theory of subadditive stochastic processes, J. Roy. Statist. Soc. Ser. B 30 (1968) 499–510
W. Kliemann, Recurrence and invariant measures for degenerate diffusions, Ann. Probab. 15 (1987) 690–707
W. Klingenberg, Riemannian Geometry, de Gruyter, Berlin 1982
O. Knill, Positive Lyapunov exponents for a dense set of bounded measurable Sl(2,ℝ) cocycles, Preprint, Zürich 1990
H. Kunita, Stochastic Differential Equations and Stochastic Flows of Diffeomorphisms, pp. 143–303 in Ecole d'Eté de Probabilités de Saint-Flour 1982, Lecture Notes in Mathematics 1097. Springer, Berlin 1984
H. Kunita, Lectures on Stochastic Flows and Applications, Tata Institute of Fundamental Research, Bombay. Springer, Berlin 1986
H. Kunita, Stochastic Flows and Stochastic Differential Equations, Cambridge University Press 1990
F. Ledrappier and P. Walters, A relativised variational principle for continuous transformations, J. London Math. Soc. (2), 16 (1977) 568–576
T. Ohno, Asymptotic behaviors of dynamical systems with random parameters, Publ. RIMS, Kyoto Univ. 19 (1983) 83–98
V.I. Oseledec, A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems. Trans. Moscow Math. Soc. 19 (1968) 197–231
D. Ruelle, Ergodic theory of differentiable dynamical systems, Publ. Math. I.H.E.S. 50 (1979) 27–58
A.D. Wentzell, Theorie zufälliger Prozesse. Akademie-Verlag, Berlin 1979
Xu Kedai, Normalformen für zufällige dynamische Systeme, Dissertation, Universität Bremen 1990
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© 1991 Springer-Verlag
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Arnold, L., Crauel, H. (1991). Random dynamical systems. In: Arnold, L., Crauel, H., Eckmann, JP. (eds) Lyapunov Exponents. Lecture Notes in Mathematics, vol 1486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086654
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DOI: https://doi.org/10.1007/BFb0086654
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