@article{AIHPB_1996__32_1_69_0,
author = {Mohammed, Salah-Eldin A. and Scheutzow, Michael K. R.},
title = {Lyapunov exponents of linear stochastic functional differential equations driven by semimartingales. {Part} {I} : the multiplicative ergodic theory},
journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
pages = {69--105},
publisher = {Gauthier-Villars},
volume = {32},
number = {1},
year = {1996},
mrnumber = {1373727},
zbl = {0862.60044},
language = {en},
url = {http://archive.numdam.org/item/AIHPB_1996__32_1_69_0/}
}
TY - JOUR AU - Mohammed, Salah-Eldin A. AU - Scheutzow, Michael K. R. TI - Lyapunov exponents of linear stochastic functional differential equations driven by semimartingales. Part I : the multiplicative ergodic theory JO - Annales de l'I.H.P. Probabilités et statistiques PY - 1996 SP - 69 EP - 105 VL - 32 IS - 1 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPB_1996__32_1_69_0/ LA - en ID - AIHPB_1996__32_1_69_0 ER -
%0 Journal Article %A Mohammed, Salah-Eldin A. %A Scheutzow, Michael K. R. %T Lyapunov exponents of linear stochastic functional differential equations driven by semimartingales. Part I : the multiplicative ergodic theory %J Annales de l'I.H.P. Probabilités et statistiques %D 1996 %P 69-105 %V 32 %N 1 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPB_1996__32_1_69_0/ %G en %F AIHPB_1996__32_1_69_0
Mohammed, Salah-Eldin A.; Scheutzow, Michael K. R. Lyapunov exponents of linear stochastic functional differential equations driven by semimartingales. Part I : the multiplicative ergodic theory. Annales de l'I.H.P. Probabilités et statistiques, Tome 32 (1996) no. 1, pp. 69-105. http://archive.numdam.org/item/AIHPB_1996__32_1_69_0/
[1] and , Large deviations of linear stochastic differential equations, H. J. ENGELBERT and W. SCHMIDT Eds., Stochastic Differential Systems, Lecture Notes in Control and Information Sciences, Vol. 96, 1987, pp. 117-151. | Zbl
[2] , and , Lyapunov exponents of linear stochastic systems, Lecture Notes in Mathematics, Vol. 1186, Springer, Berlin, 1986, pp. 85-125. | MR | Zbl
[3] , Moment stability and large deviations for linear stochastic differential equations, in: N. IKEDA Ed., Proceedings of the Taniguchi Symposium on Probabilistic Methods in Mathematical Physics, Katata and Kyoto, 1985, pp. 31-54, Tokyo, Kinokuniya, 1987. | MR | Zbl
[4] , General Topology, Part 2, Hermann, Paris, 1966. | Zbl
[5] and , Probabilités et Potentiel 1: Chapters 1-4, 2: Chapters 5-8, 2e ed., Hermann, Paris, 1980. | MR
[6] and , Méthodes de martingales et théorie des flots, Z. Wahrsch. Verw. Gebiete, Vol. 18, 1971, pp. 116-140. | MR | Zbl
[7] and , Questions de théorie des flots, Sém. de Probab. IX, Lecture Notes in Mathematics, Vol. 465, Springer, Berlin, 1975, pp. 1-96. | Numdam | Zbl
[8] , On the existence and unicity of solutions of stochastic integral equations, Z. Wahrsch. Verw. Gebiete, Vol. 36, 1976, pp. 93-101. | MR | Zbl
[9] , Stochastic Calculus and Applications, Springer, New York, Heidelberg, Berlin, 1982. | MR | Zbl
[10] , Stochastic Stability of Differential Equations, Alphen: Sijthoff and Noordhoof, 1980. | MR
[11] and , Abstract Harmonic Analysis, Academic Press and Springer, 1963. | MR
[12] and , Stochastic Differential Equations and Diffusion Processes, North Holland-Kodansha, 1989. | MR | Zbl
[13] and , On stationary solutions of a stochastic differential equation, J. Math. Kyoto University, Vol. 4, 1964, pp. 1-75. | MR | Zbl
[14] , Équations différentielles stochastiques linéaires : La méthode de variation des constantes, Séminaire de Probabilités XVI, Lecture Notes in Mathematics, Vol. 920, Springer, Berlin, 1982, pp. 442-446. | Numdam | MR | Zbl
[15] , Calcul stochastique et problème de martingales, Lecture Notes in Mathematics, Vol. 714, Springer, Berlin, Heidelberg, New York, 1979. | MR | Zbl
[16] and , Almost sure stability of linear stochastic systems with Poisson process coefficients, SIAM J. Appl. Math., Vol. 46, 1986, pp. 875-911. | MR | Zbl
[17] , Flot d'une équation différentielle stochastique avec semi-martingale directrice discontinue, Séminaire de Probabilités XIX, Lecture Notes in Mathematics, Vol. 1123, Springer, 1984, pp. 271-275. | Numdam | MR | Zbl
[18] , Stability of motions of a system with random retardations, Differential'nye Uraveneniya, Vol. 1, 1965, pp. 96-101. | MR | Zbl
[19] and , Stochastic Integration, Academic Press, New York, London, Toronto, Sydney, San Francisco, 1980. | MR | Zbl
[20] , Semimartingales, a Course on Stochastic Processes, Walter de Gruyter, Berlin, New York, 1982. | MR | Zbl
[21] , Un Cours sur les intégrales stochastiques, Séminaire de Probab. X., Lecture Notes in Math., Vol. 511, Springer, Berlin-Heidelberg-New York, 1976. | Numdam | MR | Zbl
[22] , Stochastic Functional Differential Equations, Research Notes in Mathematics No. 99, Pitman Advanced Publishing Program, Boston-London-Melboume, 1984. | MR | Zbl
[23] , The Lyapunov spectrum and stable manifolds for stochastic linear delay equations, Stochastics and Stochastic Reports, Vol. 29, 1990, pp. 89-131. | Zbl
[24] , On the existence, uniqueness, convergence and explosions of solutions of systems of stochastic integral equations, Ann. Prob., Vol. 5, 1977, pp. 243-261. | MR | Zbl
[25] , Semimartingales and measure preserving flows, Ann. Inst. Henri Poincaré, Probabilités et Statistiques, Vol. 22, 1986, pp. 127-147. | Numdam | MR | Zbl
[26] , Stochastic Integration and Differential Equations, Springer, 1990. | MR | Zbl
[27] , Ergodic theory of differentiable dynamical systems, I.H.E.S. Publications, Vol. 50, 1979, pp. 275-305. | Numdam | MR | Zbl
[28] , Characteristic exponents and invariant manifolds in Hilbert space, Annals of Mathematics, Vol. 115, 1982, pp. 243-290. | MR | Zbl
