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1. | Institut für Mathematik, Technische Universität Berlin, Str. des 17. Juni 136, 10623 Berlin |
References:
[1] |
L. Arnold, W. Kliemann and E. Oeljeklaus, Lyapunov exponents for linear stochastic systems, in "Lyapunov Exponents'' (eds. L. Arnold and V. Wihstutz) (Breman, 1984), Lecture Notes in Math., 1186, Springer, Berlin, (1986), 85-125.
doi: 10.1007/BFb0076836. |
[2] |
G. Da Prato and J. Zabczyk, "Ergodicity for Infinite Dimensional Systems," London Mathematical Society Lecture Note Series, 229, Cambridge University Press, Cambridge, 1996.
doi: 10.1017/CBO9780511662829. |
[3] |
H. Furstenberg, Noncommuting random products, Trans. Amer. Math. Soc., 108 (1963), 377-428. |
[4] |
M. Hairer, J. Mattingly and M. Scheutzow, Asymptotic coupling and a general form of Harris' theorem with applications to stochastic delay equations, Prob. Theory Rel. Fields, 149 (2011), 223-259.
doi: 10.1007/s00440-009-0250-6. |
[5] |
P. Hall and C. Heyde, "Martingale Limit Theory and its Application," Probability and Mathematical Statistics, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980. |
[6] |
R. Z. Has'minskiĭ, Necessary and sufficient conditions for asymptotic stability of linear stochastic systems, Theory Probability Appl., 12 (1967), 144-147. |
[7] |
R. S. Liptser and A. N. Shiryayev, "Statistics of Random Processes. I. General Theory," Translated by A. B. Aries, Applications of Mathematics, Vol. 5, Springer-Verlag, New York-Heidelberg, 1977. |
[8] |
S. Mohammed, Nonlinear flows of stochastic linear delay equations, Stochastics, 17 (1986), 207-213.
doi: 10.1080/17442508608833390. |
[9] |
S. Mohammed and M. Scheutzow, Lyapunov exponents of linear stochastic functional differential equations driven by semimartingales. I. The multiplicative ergodic theory, Ann. Inst. H. Poincaré Probab. Statist., 32 (1996), 69-105. |
[10] |
S. Mohammed and M. Scheutzow, Lyapunov exponents of linear stochastic functional differential equations driven by semimartingales. II. Examples and case studies, Ann. Probab., 25 (1997), 1210-1240.
doi: 10.1214/aop/1024404511. |
[11] |
M. Scheutzow, Exponential growth rates for stochastic delay differential equations, Stoch. Dyn., 5 (2005), 163-174.
doi: 10.1142/S0219493705001468. |
show all references
References:
[1] |
L. Arnold, W. Kliemann and E. Oeljeklaus, Lyapunov exponents for linear stochastic systems, in "Lyapunov Exponents'' (eds. L. Arnold and V. Wihstutz) (Breman, 1984), Lecture Notes in Math., 1186, Springer, Berlin, (1986), 85-125.
doi: 10.1007/BFb0076836. |
[2] |
G. Da Prato and J. Zabczyk, "Ergodicity for Infinite Dimensional Systems," London Mathematical Society Lecture Note Series, 229, Cambridge University Press, Cambridge, 1996.
doi: 10.1017/CBO9780511662829. |
[3] |
H. Furstenberg, Noncommuting random products, Trans. Amer. Math. Soc., 108 (1963), 377-428. |
[4] |
M. Hairer, J. Mattingly and M. Scheutzow, Asymptotic coupling and a general form of Harris' theorem with applications to stochastic delay equations, Prob. Theory Rel. Fields, 149 (2011), 223-259.
doi: 10.1007/s00440-009-0250-6. |
[5] |
P. Hall and C. Heyde, "Martingale Limit Theory and its Application," Probability and Mathematical Statistics, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980. |
[6] |
R. Z. Has'minskiĭ, Necessary and sufficient conditions for asymptotic stability of linear stochastic systems, Theory Probability Appl., 12 (1967), 144-147. |
[7] |
R. S. Liptser and A. N. Shiryayev, "Statistics of Random Processes. I. General Theory," Translated by A. B. Aries, Applications of Mathematics, Vol. 5, Springer-Verlag, New York-Heidelberg, 1977. |
[8] |
S. Mohammed, Nonlinear flows of stochastic linear delay equations, Stochastics, 17 (1986), 207-213.
doi: 10.1080/17442508608833390. |
[9] |
S. Mohammed and M. Scheutzow, Lyapunov exponents of linear stochastic functional differential equations driven by semimartingales. I. The multiplicative ergodic theory, Ann. Inst. H. Poincaré Probab. Statist., 32 (1996), 69-105. |
[10] |
S. Mohammed and M. Scheutzow, Lyapunov exponents of linear stochastic functional differential equations driven by semimartingales. II. Examples and case studies, Ann. Probab., 25 (1997), 1210-1240.
doi: 10.1214/aop/1024404511. |
[11] |
M. Scheutzow, Exponential growth rates for stochastic delay differential equations, Stoch. Dyn., 5 (2005), 163-174.
doi: 10.1142/S0219493705001468. |
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