Stratonovich stochastic differential equations driven by general semimartingales
Annales de l'I.H.P. Probabilités et statistiques, Volume 31 (1995) no. 2, p. 351-377
@article{AIHPB_1995__31_2_351_0,
     author = {Kurtz, Thomas G. and Pardoux, \'Etienne and Protter, Philip},
     title = {Stratonovich stochastic differential equations driven by general semimartingales},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {31},
     number = {2},
     year = {1995},
     pages = {351-377},
     zbl = {0823.60046},
     mrnumber = {1324812},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1995__31_2_351_0}
}
Kurtz, Thomas G.; Pardoux, Étienne; Protter, Philip. Stratonovich stochastic differential equations driven by general semimartingales. Annales de l'I.H.P. Probabilités et statistiques, Volume 31 (1995) no. 2, pp. 351-377. http://www.numdam.org/item/AIHPB_1995__31_2_351_0/

[1] E. Çinlar, J. Jacod, P. Protter and M. Sharpe, Semimartingales and Markov Processes, Z. für Wahrscheinlichkeitstheorie, Vol. 54, 1980, pp. 161-220. | MR 597337 | Zbl 0443.60074

[2] S. Cohen, Géométrie différentielle stochastique avec sauts, C. R. Acad. Sci. Paris, Vol. 314, 1992, pp. 767-770. | MR 1163874 | Zbl 0757.60048

[3] C. Dellacherie and P.A. Meyer, Probabilities and Potential B, North Holland, Amsterdam, 1982. | MR 745449 | Zbl 0494.60002

[4] A. Estrade, Exponentielle stochastique et intégrale multiplicative discontinue, to appear in Ann. Inst. H. Poincaré, 1992. | Numdam | MR 1158740 | Zbl 0760.60048

[5] T. Fujiwara, Stochastic differential equations of jump type on manifolds and Lévy flows, J. Math. Kyoto Univ., Vol. 31, 1991, pp. 99-119. | MR 1093330 | Zbl 0728.60065

[6] J. Jacod and P. Protter, Une remarque sur les équations différentielles stochastiques à solutions Markoviennes, in Séminaire de Probabilités XXV, Springer Lect. Notes in Math., 1485, 1991, pp. 138-139. | Numdam | MR 1187777 | Zbl 0741.60051

[7] M.W. Hirsch, Differential Topology, Springer-Verlag, New York, Berlin, 1976. | MR 448362 | Zbl 0356.57001

[8] T.G. Kurtz, Random time changes and convergence in distribution under the Meyer-Zheng conditions, Annals of Probability, Vol. 19, 1991, pp. 1010-1034. | MR 1112405 | Zbl 0742.60036

[9] T.G. Kurtz and P. Protter, Weak limit theorems for stochastic integrals and stochastic differential equations, Annals of Probability, Vol. 19, 1991, pp. 1035-1070. | MR 1112406 | Zbl 0742.60053

[10] T.G. Kurtz and P. Protter, Characterizing the weak convergence of stochastic integrals, in Stochastic Analysis, M. Barlow and N. Bingham, Eds., 1991, pp. 255-259. | MR 1166413 | Zbl 0738.60053

[11] T.G. Kurtz and P. Protter, Wong-Zakai corrections, random evolutions, and simulation schemes for SDE's, Stochastic Analysis: Liber Amicorum for Moshe Zakai, Academic Press, San Diego, 1991, pp. 331-346. | MR 1119837 | Zbl 0762.60047

[12] H.J. Kushner, Jump-diffusion approximations for ordinary differential equations with wide-band random right hand sides, SIAM J. Control, Vol. 17, 1979, pp. 729-744. | MR 548701 | Zbl 0432.60096

[13] S.I. Marcus, Modeling and analysis of stochastic differential equations driven by point processes, IEEE Transactions on Information Theory, Vol. 24, 1978, pp. 164-172. | MR 487784 | Zbl 0372.60084

[14] S.I. Marcus, Modeling and approximation of stochastic differential equations driven by semimartingales, Stochastics, Vol. 4, 1981, pp. 223-245. | MR 605630 | Zbl 0456.60064

[15] M. Métivier, Semimartingales: a course on stochastic processes, de Gruyter, Berlin, New York, 1982. | MR 688144 | Zbl 0503.60054

[16] P.A. Meyer, Un cours sur les intégrales stochastiques, Séminaire Proba. X, Lecture Notes in Mathematics, Vol. 511, pp. 246-400, Springer-Verlag, Berlin, New York, 1976. | Numdam | MR 501332 | Zbl 0374.60070

[17] P. Protter, Stochastic integration and differential equations: a new approach, Springer-Verlag, Berlin, New York, 1990. | MR 1037262 | Zbl 0694.60047

[18] E. Wong and M. Zakai, On the convergence of ordinary integrals to stochastic integrals, Ann. Math. Statist., Vol. 36, 1965, pp. 1560-1564. | MR 195142 | Zbl 0138.11201