stability of solutions of symmetric stochastic differential equations with discontinuous driving semimartingales
Annales de l'I.H.P. Probabilités et statistiques (1987)
- Volume: 23, Issue: 4, page 575-592
- ISSN: 0246-0203
Access Full Article
topHow to cite
topMackevičius, Vigirdas. "$S^p$ stability of solutions of symmetric stochastic differential equations with discontinuous driving semimartingales." Annales de l'I.H.P. Probabilités et statistiques 23.4 (1987): 575-592. <http://eudml.org/doc/77305>.
@article{Mackevičius1987,
author = {Mackevičius, Vigirdas},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {stability; stochastic integral equation; cadlag semi-martingale},
language = {eng},
number = {4},
pages = {575-592},
publisher = {Gauthier-Villars},
title = {$S^p$ stability of solutions of symmetric stochastic differential equations with discontinuous driving semimartingales},
url = {http://eudml.org/doc/77305},
volume = {23},
year = {1987},
}
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
PB - Gauthier-Villars
VL - 23
IS - 4
SP - 575
EP - 592
LA - eng
KW - stability; stochastic integral equation; cadlag semi-martingale
UR - http://eudml.org/doc/77305
ER -
References
top- [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. Zbl0464.60001MR488194
- [3] H. Doss, Liens entre équations différentielles stochastiques et ordinaires, Ann. Inst. Henri Poincaré, T. 13, n° 2, 1977, pp. 99-125. Zbl0359.60087MR451404
- [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. Zbl0351.60054MR464400
- [5] M. Emery, Equations différentielles lipschitziennes: étude de la stabilité, Lect. Notes in Mathematics, T. 721, 1979, pp. 281-293. Zbl0408.60064MR544801
- [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. Zbl0376.93024MR482999
- [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. Zbl0513.60058MR799933
- [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. Zbl0391.60055MR458587
- [9] N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North Holland-Kodansha, Amsterdam-Tokyo, 1981. Zbl0495.60005MR637061
- [10] F. Konecny, On Wong-Zakai Approximation of Stochastic Differential Equations, J. Multivariate Anal, T. 13, No. 4, 1983, pp. 605-611. Zbl0535.60053MR727043
- [11] A.J. Krener, A Formal Approach to Stochastic Integration and Differential Equations, Stochastics, T. 3, 1979, pp. 105-125. Zbl0435.60051MR553908
- [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. Zbl0659.60086MR823204
- [13] S.I. Marcus, Modeling and Approximation of Stochastic Differential Equations Driven by Semimartingales, Stochastics, T. 4, No. 3, 1981, pp. 223-245. Zbl0456.60064MR605630
- [14] E.J. Mcshane, Stochastic Calculus and Stochastic Models, Academic Press, New York, 1974. Zbl0292.60090MR443084
- [15] E.J. Mcshane, Stochastic Differential Equations, J. Multivariate Anal., T. 5, 1975, pp. 121-177. Zbl0323.60059MR373006
- [16] M. Metivier and J. Pellaumail, Stochastic Integration, Academic Press, New York, 1980. Zbl0463.60004MR578177
- [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. Zbl0426.60059MR556417
- [18] P.-A. Meyer, Un cours sur les intégrales stochastiques, Lect. Notes in Math., T. 511, 1976, pp. 245-400. Zbl0374.60070MR501332
- [19] P.-A. Meyer, Inégalités de normes pour les intégrales stochastiques, Lect. Notes in Math., T. 649, 1978, pp. 757-762. Zbl0382.60050MR520043
- [20] S. Nakao and Y. Yamato, Approximation Theorem on Stochastic Differential Equations, Proc. Internat. Symp., S.D.E., Kyotô, 1976, pp. 283-296. Zbl0443.60051MR536015
- [21] P. Protter, Hp Stability of Solutions of Stochastic Differential Equations, Z. Wahrsch. v. Geb., T. 44, 1978, pp. 337-352. Zbl0378.60042MR509206
- [22] P. Protter, Approximations of Solutions of Stochastic Differential Equations Driven by Semimartingales, Ann. Probab., T. 13, No. 3, 1985, pp. 716-743. Zbl0578.60055MR799419
- [23] H.J. Sussmann, On the Gap Between Deterministic and Stochastic Ordinary Differential Equations, Ann. Probab., T. 6, 1978, pp. 19-41. Zbl0391.60056MR461664
- [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. Zbl0138.11201MR195142
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.