Stratonovich stochastic differential equations driven by general semimartingales

Thomas G. Kurtz; Étienne Pardoux; Philip Protter

Annales de l'I.H.P. Probabilités et statistiques (1995)

  • Volume: 31, Issue: 2, page 351-377
  • ISSN: 0246-0203

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Kurtz, Thomas G., Pardoux, Étienne, and Protter, Philip. "Stratonovich stochastic differential equations driven by general semimartingales." Annales de l'I.H.P. Probabilités et statistiques 31.2 (1995): 351-377. <http://eudml.org/doc/77513>.

@article{Kurtz1995,
author = {Kurtz, Thomas G., Pardoux, Étienne, Protter, Philip},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {stochastic differential equations; semimartingale; change of variable formula holds; Stratonovich equation},
language = {eng},
number = {2},
pages = {351-377},
publisher = {Gauthier-Villars},
title = {Stratonovich stochastic differential equations driven by general semimartingales},
url = {http://eudml.org/doc/77513},
volume = {31},
year = {1995},
}

TY - JOUR
AU - Kurtz, Thomas G.
AU - Pardoux, Étienne
AU - Protter, Philip
TI - Stratonovich stochastic differential equations driven by general semimartingales
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1995
PB - Gauthier-Villars
VL - 31
IS - 2
SP - 351
EP - 377
LA - eng
KW - stochastic differential equations; semimartingale; change of variable formula holds; Stratonovich equation
UR - http://eudml.org/doc/77513
ER -

References

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  2. [2] S. Cohen, Géométrie différentielle stochastique avec sauts, C. R. Acad. Sci. Paris, Vol. 314, 1992, pp. 767-770. Zbl0757.60048MR1163874
  3. [3] C. Dellacherie and P.A. Meyer, Probabilities and Potential B, North Holland, Amsterdam, 1982. Zbl0494.60002MR745449
  4. [4] A. Estrade, Exponentielle stochastique et intégrale multiplicative discontinue, to appear in Ann. Inst. H. Poincaré, 1992. Zbl0760.60048MR1158740
  5. [5] T. Fujiwara, Stochastic differential equations of jump type on manifolds and Lévy flows, J. Math. Kyoto Univ., Vol. 31, 1991, pp. 99-119. Zbl0728.60065MR1093330
  6. [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. Zbl0741.60051MR1187777
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  9. [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. Zbl0742.60053MR1112406
  10. [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. Zbl0738.60053MR1166413
  11. [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. Zbl0762.60047MR1119837
  12. [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. Zbl0432.60096MR548701
  13. [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. Zbl0372.60084MR487784
  14. [14] S.I. Marcus, Modeling and approximation of stochastic differential equations driven by semimartingales, Stochastics, Vol. 4, 1981, pp. 223-245. Zbl0456.60064MR605630
  15. [15] M. Métivier, Semimartingales: a course on stochastic processes, de Gruyter, Berlin, New York, 1982. Zbl0503.60054MR688144
  16. [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. Zbl0374.60070MR501332
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  18. [18] E. Wong and M. Zakai, On the convergence of ordinary integrals to stochastic integrals, Ann. Math. Statist., Vol. 36, 1965, pp. 1560-1564. Zbl0138.11201MR195142

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