S p stability of solutions of symmetric stochastic differential equations with discontinuous driving semimartingales
Annales de l'I.H.P. Probabilités et statistiques, Tome 23 (1987) no. 4, pp. 575-592. 
@article{AIHPB_1987__23_4_575_0,
     author = {Mackevi\v{c}ius, Vigirdas},
     title = {$S^p$ stability of solutions of symmetric stochastic differential equations with discontinuous driving semimartingales},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {575--592},
     publisher = {Gauthier-Villars},
     volume = {23},
     number = {4},
     year = {1987},
     mrnumber = {928004},
     zbl = {0636.60057},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1987__23_4_575_0/}
}
TY  - JOUR
AU  - Mackevičius, Vigirdas
TI  - $S^p$ stability of solutions of symmetric stochastic differential equations with discontinuous driving semimartingales
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 1987
SP  - 575
EP  - 592
VL  - 23
IS  - 4
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPB_1987__23_4_575_0/
LA  - en
ID  - AIHPB_1987__23_4_575_0
ER  - 
%0 Journal Article
%A Mackevičius, Vigirdas
%T $S^p$ stability of solutions of symmetric stochastic differential equations with discontinuous driving semimartingales
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1987
%P 575-592
%V 23
%N 4
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPB_1987__23_4_575_0/
%G en
%F AIHPB_1987__23_4_575_0
Mackevičius, Vigirdas. $S^p$ stability of solutions of symmetric stochastic differential equations with discontinuous driving semimartingales. Annales de l'I.H.P. Probabilités et statistiques, Tome 23 (1987) no. 4, pp. 575-592. http://www.numdam.org/item/AIHPB_1987__23_4_575_0/

[1] M.-F. Allain, Sur quelques types d'approximations des solutions d'équations différentielles stochastiques, Thèse, Université de Rennes, 1974.

[2] C. Dellacherie and P.-A. Meyer, Probabilités et Potentiel, Hermann, Paris, 1980. | MR

[3] H. Doss, Liens entre équations différentielles stochastiques et ordinaires, Ann. Inst. Henri Poincaré, T. 13, n° 2, 1977, pp. 99-125. | Numdam | MR | Zbl

[4] M. Emery, Stabilité des solutions des equations différentielles stochastiques: application aux intégrales multiplicatives stochastiques, Z. Wahrsch. v. Geb., T. 41, No. 3, 1978, pp. 241-262. | MR | Zbl

[5] M. Emery, Equations différentielles lipschitziennes: étude de la stabilité, Lect. Notes in Mathematics, T. 721, 1979, pp. 281-293. | Numdam | MR | Zbl

[6] M.I. Freedman and J.C. Willems, Smooth Representation of Systems with Differentiated Inputs, I.E.E.E. Trans. Aut. Control, T. AC-23, 1978, pp. 16-21. | MR | Zbl

[7] B. Grigelionis and R. Mikulevicius, Stochastic Evolution Equations and Densities of the Conditional Distributions, Lect. Notes in Control and Inf. Sc., T. 49, 1984, pp. 49-88. | MR | Zbl

[8] N. Ikeda, S. Nakao and Y. Yamato, A Class of Approximations of Brownian Motion, Publ. Res. Inst. Math. Sc., T. 13, No. 1, 1977, pp. 285-300. | MR | Zbl

[9] N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North Holland-Kodansha, Amsterdam-Tokyo, 1981. | MR | Zbl

[10] F. Konecny, On Wong-Zakai Approximation of Stochastic Differential Equations, J. Multivariate Anal, T. 13, No. 4, 1983, pp. 605-611. | MR | Zbl

[11] A.J. Krener, A Formal Approach to Stochastic Integration and Differential Equations, Stochastics, T. 3, 1979, pp. 105-125. | MR | Zbl

[12] V. Mackevičius, Sp Stability of Solutions of Symmetric Stochastic Differential Equations, Lietuvos Matematikos Rinkinys, T. 25, No. 4, 1985, pp. 72-84 (in Russian). English translation to appear in Lithuanian Math. J. | MR | Zbl

[13] S.I. Marcus, Modeling and Approximation of Stochastic Differential Equations Driven by Semimartingales, Stochastics, T. 4, No. 3, 1981, pp. 223-245. | MR | Zbl

[14] E.J. Mcshane, Stochastic Calculus and Stochastic Models, Academic Press, New York, 1974. | MR | Zbl

[15] E.J. Mcshane, Stochastic Differential Equations, J. Multivariate Anal., T. 5, 1975, pp. 121-177. | MR | Zbl

[16] M. Metivier and J. Pellaumail, Stochastic Integration, Academic Press, New York, 1980. | MR | Zbl

[17] M. Metivier and J. Pellaumail, On a Stopped Doob's Inequality and General Stochastic Equations, Ann. Probab., T. 8, No. 1, 1980, pp. 96-114. | MR | Zbl

[18] P.-A. Meyer, Un cours sur les intégrales stochastiques, Lect. Notes in Math., T. 511, 1976, pp. 245-400. | Numdam | MR | Zbl

[19] P.-A. Meyer, Inégalités de normes pour les intégrales stochastiques, Lect. Notes in Math., T. 649, 1978, pp. 757-762. | Numdam | MR | Zbl

[20] S. Nakao and Y. Yamato, Approximation Theorem on Stochastic Differential Equations, Proc. Internat. Symp., S.D.E., Kyotô, 1976, pp. 283-296. | MR | Zbl

[21] P. Protter, Hp Stability of Solutions of Stochastic Differential Equations, Z. Wahrsch. v. Geb., T. 44, 1978, pp. 337-352. | MR | Zbl

[22] P. Protter, Approximations of Solutions of Stochastic Differential Equations Driven by Semimartingales, Ann. Probab., T. 13, No. 3, 1985, pp. 716-743. | MR | Zbl

[23] H.J. Sussmann, On the Gap Between Deterministic and Stochastic Ordinary Differential Equations, Ann. Probab., T. 6, 1978, pp. 19-41. | MR | Zbl

[24] E. Wong and M. Zakai, On the Convergence of Ordinary Integrals to Stochastic Integrals, Ann. Math. Statist., T. 36, No. 5, 1965, pp. 1560-1564. | MR | Zbl