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Calcul des variations stochastique et processus de sauts. (French) Zbl 0494.60082

MSC:
60J75 Jump processes (MSC2010)
60H05 Stochastic integrals
65H10 Numerical computation of solutions to systems of equations
60J35 Transition functions, generators and resolvents
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[1] Bismut, J.M.: Mécanique aléatoire. Lecture Notes in Math. 866. Berlin-Heidelberg-New York: Springer 1981
[2] Bismut, J.M.: A generalized formula of Ito and some other properties of stochastic flows. Z. Wahrscheinlichkeitstheorie verw. Gebiete 55, 331-350 (1981) · Zbl 0456.60063 · doi:10.1007/BF00532124
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[13] Kesten, H.: Hitting probabilities of single points for processes with independent increments. Memoir Amer. Math. Soc. no. 93, 1-129 (1969) · Zbl 0186.50202
[14] Malliavin, P.: Stochastic calculus of variations and hypoelliptic operators. Proc. Intern. Conf. on Stochastic differential equations of Kyoto 1976, 195-263. Tokyo-Kinokuniya and New York: Wiley 1978 · Zbl 0411.60060
[15] Malliavin, P.: C k hypoellipticity with degeneracy. Stochastic analysis, ed. A. Friedman and M. Pinsky, 199-214. New York-London: Acad. Press 1978
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[20] Stroock, D.W.: The Malliavin calculus and its applications. In: Stochastic Integrals, ed. D. Williams, pp. 394-432. Lecture Notes in Math. 851. Berlin-Heidelberg-New York: Springer 1981 · Zbl 0459.60052
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[22] Tucker, H.G.: Absolute continuity of infinitely divisible distributions. Pacific J. Math. 12, 1125-1129 (1962) · Zbl 0109.36503
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[24] Williams, D.: To begin at the beginning. In: Stochastic Integrals, ed. D. Williams. Lecture Notes in Math. 851, pp. 1-55. Berlin-Heidelberg-New York: Springer 1981 · Zbl 0471.60065
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[27] Hartman, P., Wintner, A.: The infinitesimal generator of integral convolution. Amer. J. Math. 64, 273-298 (1942) · Zbl 0063.01951 · doi:10.2307/2371683
[28] Doleans-Dade, C.: Quelques applications de la formule de changement de variables pour les semi-martingales. Z. Wahrscheinlichkeitstheorie verw. Gebiete 16, 181-194 (1970) · Zbl 0201.19503 · doi:10.1007/BF00534595
[29] Billingsley, P.: Convergence of probability measures. New York: Wiley 1968 · Zbl 0172.21201
[30] Jacod, J., Yor, M.: Étude des solutions extrémales et représentation intégrale des solutions pour certains problèmes de martingales. Z. Wahrscheinlichkeitstheorie verw. Gebiete 38, 83-125 (1977) · Zbl 0346.60032 · doi:10.1007/BF00533303
[31] Kobayashi, S., Nomizu, K.: Foundations of differential geometry. Vol. I. New York: Interscience 1963 · Zbl 0119.37502
[32] Karamata, J.: Neuer Beweis und verallgemeinerung der Tauberschen Sätze, welche die Laplacesche und Stieltjessche Transformation betreffen. J. Reine Angew. Math. 164, 27-39 (1931) · JFM 57.0262.01 · doi:10.1515/crll.1931.164.27
[33] Bismut, J.M.: The calculus of boundary processes. To appear · Zbl 0561.60081
[34] Bismut, J.M.: Calcul des variations sur les processus de sauts. C.R. Acad. Sci. Paris, Série I, 293, 565-568 (1981) · Zbl 0484.60067
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