Introduction au calcul stochastique

Yor, Marc

Séminaire Bourbaki : volume 1981/82, exposés 579-596, Astérisque, no. 92-93 (1982), Exposé no. 590, 18 p.

MR Zbl | 2 citations dans Numdam

@incollection{SB_1981-1982__24__275_0,
     author = {Yor, Marc},
     title = {Introduction au calcul stochastique},
     booktitle = {S\'eminaire Bourbaki : volume 1981/82, expos\'es 579-596},
     series = {Ast\'erisque},
     note = {talk:590},
     pages = {275--292},
     year = {1982},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {92-93},
     mrnumber = {689534},
     zbl = {0497.60055},
     language = {fr},
     url = {https://www.numdam.org/item/SB_1981-1982__24__275_0/}
}

TY  - CHAP
AU  - Yor, Marc
TI  - Introduction au calcul stochastique
BT  - Séminaire Bourbaki : volume 1981/82, exposés 579-596
AU  - Collectif
T3  - Astérisque
N1  - talk:590
PY  - 1982
SP  - 275
EP  - 292
IS  - 92-93
PB  - Société mathématique de France
UR  - https://www.numdam.org/item/SB_1981-1982__24__275_0/
LA  - fr
ID  - SB_1981-1982__24__275_0
ER  -

%0 Book Section
%A Yor, Marc
%T Introduction au calcul stochastique
%B Séminaire Bourbaki : volume 1981/82, exposés 579-596
%A Collectif
%S Astérisque
%Z talk:590
%D 1982
%P 275-292
%N 92-93
%I Société mathématique de France
%U https://www.numdam.org/item/SB_1981-1982__24__275_0/
%G fr
%F SB_1981-1982__24__275_0

Yor, Marc. Introduction au calcul stochastique, dans Séminaire Bourbaki : volume 1981/82, exposés 579-596, Astérisque, no. 92-93 (1982), Exposé no. 590, 18 p.. https://www.numdam.org/item/SB_1981-1982__24__275_0/

Bibliographie
Cité par

[1] K. D. Elworthy - Stochastic methods and differential geometry, Séminaire Bourbaki 1980/81, Springer-Verlag, Lecture Notes in Math. 901(1981), 95-110. | Zbl | MR | Numdam

[2] B. Davis - Brownian Motion and analytic functions, Annals of Proba. 7(1979), n° 6, 913-932. | Zbl | MR

[3] A. M. Garsia, E. Rodemich, H. Rumsey Jr - A real variable lemma and the continuity of paths of some gaussian processes, Indiana Univ. Math. J. 20(1970/71), 565-578. | Zbl | MR

[4] J. Neveu - Bases mathématiques du calcul des probabilités, 2e édition, Masson, 1970. | Zbl | MR

[5] D. W. Stroock, S. R. S. Varadhan - Multidimensional diffusion processes, Springer, 1979. | Zbl | MR

[6] A. M. Garsia - Combinatorial inequalities and smoothness of functions, Bull. Amer. Math. Soc., 82, n°2(March 1976), 157-170. | Zbl | MR

[7] W. J. Park - A multiparameter gaussian process, Ann. Math. Stat. 41(1970), 1582-1595. | Zbl | MR

[8] R. Cairoli, J. B. Walsh - Stochastic integrals in the plane, Acta Math. 134 (1975), 111-183. | Zbl | MR

[9] P. Lévy - Processus stochastiques et mouvement brownien, Gauthiers-Villars, 1965. | Zbl | MR

[10] H. Kunita, S. Watanabe - On square integrable martingales, Nagoya Math. J. 30(1967), 209-245. | Zbl | MR

[11] P. A. Meyer - Probabilités et potentiel, Hermann, 1966. | Zbl | MR

[12] J. Pellaumail - Sur l'intégrale stochastique et la décomposition de Doob-Meyer, Soc. Math. France, Astérisque n° 9(1973). | Zbl | MR | Numdam

[13] M. Métivier, J. Pellaumail - Stochastic Integration, Academic Press, New York, 1979. | Zbl | MR

[14] A. U. Kussmaul - Stochastic integration and generalized martingales, Research Notes in Math. n° 11, Pitman (Londres), 1977. | Zbl | MR

[15] M. Yor - Quelques interactions entre mesures vectorielles et intégrales stochastiques, Sém. Th. du Potentiel n° 4(1979), Lecture Notes in Math. 713, 264-281. | Zbl | MR

[16] K. Bitcheler - Stochastic integration and Lp-theory of semimartingales, Annals of Proba. 9(1980), n° 1, 49-89. | Zbl

[17] C. Dellacherie - Un survol de la théorie de l'intégrale stochastique, Stochastic Processes and their Applications 10(1980), 115-144. | Zbl | MR

[18] P. A. Meyer - Caractérisation des semi-martingales, d'après Dellacherie, Sém. Proba. XIII, Springer-Verlag, Lect. Notes in Math. 721(1979), 620-623. | Zbl | MR | Numdam

[19] K. Dambis - On the decomposition of continuous sub-martingales, Teo. Verojatnost. 10(1965), 438-448. | Zbl | MR

[20] L. Dubins, G. Schwarz - On continuous martingales, Proc. Nat. Acad. USA, 53(1965), 913-916. | Zbl | MR

[21] F. Knight - A reduction of continuous square-integrable martingales to brownian motion, Springer-Verlag, Lect. Notes in Math. 190(1971). | MR

[22] K. Itô - Multiple Wiener integral, J. Math. Soc. Japan 3(1951), 157-169. | Zbl | MR

[23] C. Dellacherie - Intégrales stochastiques par rapport aux processus de Wiener et de Foisson, Sém. Proba. VIII, Springer-Verlag, Lect. Notes in Math. 381(1974). | Zbl | MR | Numdam

[24] J. Jacod - Calcul stochastique et problèmes de martingales, Springer-Verlag, Lect. Notes in Math. 714(1979). | Zbl | MR

[25] A. M. Garsia - Martingale inequalities, Seminar Notes on Recent Progress, Benjamin, 1973. | Zbl | MR

[26] J. Neveu - Martingales à temps discret, Masson, 1972. | MR

[27] H. P. Mckean - Stochastic integrals, Academic Press, 1969. | Zbl | MR

[28] H. P. Mckean - Brownian local times, Adv. in Math. 10(1975), 91-111. | Zbl | MR

[29] D. Ray - Sojourn times of diffusion processes, Illinois J. Math. 7(1963), 615-630 | Zbl | MR

[30] F. B. Knight - Random walks and the sojourn density process of brownian motion, Trans. Amer. Math. Soc. 109(1963), 56-86. | Zbl | MR

[31] J. Azéma, M. Yor - Une solution simple au problème de Skorokhod, Sém. Proba. XIII, Springer-Verlag, Lect. Notes in Math. 721(1979). | Zbl | MR | Numdam

[32] D. Kennedy - Some martingales related to cumulative sum tests and singleserver queues, in : Stochastic processes and their applications, 4 (1976), 261-269. | Zbl | MR

[33] T. Jeulin, M. Yor - Sur les distributions de certaines fonctionnelles du mouvement brownien, Sém. Proba. XV, Springer-Verlag, Lect. Notes in Math. 850(1981). | Zbl | MR | Numdam

[34] J. M. Bismut - Mécanique aléatoire, Springer-Verlag, Lect. Notes in Math. 866(1981). | Zbl | MR

[35] N. Ikeda, S. Manabe - Integral of differential forms along the path of diffusion processes, Publ. RIMS, Kyoto Univ. 15(1979), 827-852. | Zbl | MR

[36] R. L. Stratonovitch - Conditional Markov processes and their application to the theory of optimal control, Amer. Elsevier, New York, 1968. | Zbl | MR

[37] D. W. Stroock, S. R. S. Varadhan - Diffusion processes with continuous coefficients, I, II, Comm. Pure Appl. Math. 22(1969), 345-400, 479-530. | Zbl | MR

[38] T. Yamada, S. Watanabe - On the uniqueness of solutions of stochastic differential equations, J. Math. Kyoto Univ. 11(1971), 155-167. | Zbl | MR

[39] K. Itô - On stochastic differential equations, Mem. Amer. Math. Soc. 4(1951). | Zbl | MR

[40] S. Nakao - On the pathwise uniqueness of solutions of one-dimensional sto- chastic differential equations, Osaka J. Math. 9(1972), 513-518. | Zbl | MR

[41] D. Williams - "To begin at the beginning...", in : "Stochastic Integrals", Springer-Verlag, Lect. Notes in Math. 851(1981). | Zbl | MR

[42] J. H. Van Schuppen, E. Wong - Transformations of local martingales under a change of law, Ann. Prob. 2(1974), 879-888. | Zbl | MR

[43] I. V. Girsanov - On transforming a certain class of stochastic processes by absolutely continuous substitutions of measures, Teo. Ver. Pim 5(1960). | Zbl | MR

[44] M. Yor - Loi de l'indice du lacet brownien et distribution de Hartman-Watson, Zeitschrift für Wahr. 53(1980), 71-95. | Zbl | MR

[45] J. Pitman, M. Yor - Sur une décomposition des ponts de Bessel, Springer-Verlag, Lect. Notes in Math. 923(1982), 276-285. | Zbl | MR

[46] H. Doss - Sur une résolution stochastique de l'équation de Schrödinger à coefficients analytiques, Comm. Math. Phys. 73(1980), 247-264. | Zbl | MR

[47] K. Itô - Poisson point processes attached to Markov processes, Proc. Sixth Berkeley Symp. Math. Statist. Prob. III, 225-239, Univ. California Press, Berkeley, 1972. | Zbl | MR

[48] D. Williams - Diffusions, Markov processes, and Martingales, J. Wiley, 1979. | MR

[49] L. C. G. Rogers - Williams' characterisation of the brownian excursion law : proof and applications, Sém. Proba. XV, Springer-Verlag, Lect. Notes in Math. 850(1981). | Zbl | MR | Numdam

[50] K. Itô - Extension of stochastic integrals, Proc. of Intern. Symp. SDE Kyoto, (1976), 95-109. | Zbl | MR

[51] T. Jeulin - Semi-martingales et grossissement d'une filtration, Springer-Verlag, Lect. Notes in Math. 833, 1980. | Zbl | MR

[52] M. T. Barlow - Study of a filtration expanded to include an honest time, Zeitschrift für Wahr. 44(1978), 307-323. | Zbl | MR

[53] T. Jeulin, M. Yor - Nouveaux résultats sur le grossissement des tribus, Ann. Scient. ENS, 4e série, 11(1978), 429-443. | Zbl | MR | Numdam

[54] Ch. Yoeurp - Thèse d'Etat, Univ. P. et M. Curie, 1982.

[55] D. Williams - Path decomposition and continuity of local time for one-dimensional diffusions I, Proc. London Math. Soc. (3), 28(1974), 738-768. | Zbl | MR

[56] J. W. Pitman - One-dimensional brownian motion and the three-dimensional Bessel process, Adv. Appl. Prob. 7(1975), 511-526. | Zbl | MR

[57] T. Jeulin - Un théorème de J.W. Pitman, Sém. Proba. XIII, Springer-Verlag, Lect. Notes in Math. 721(1979), 521-532. | Zbl | MR | Numdam

[58] L. C. G. Rogers, J. W. Pitman - Markov functions, Annals of Prob. 9 (4)(1981), 573-582. | Zbl | MR

[59] N. Ikeda, S. Watanabe - Stochastic differential equations and diffusion processes, North-Holland-Kodansha, 1981. | Zbl | MR

[60] E. Nelson - Quantum fields and Markoff fields, Amer. Math. J., (1971). | MR

[61] J. Neveu - Sur l'espérance conditionnelle par rapport à un mouvement brownien, Ann. IHP, 12 (2)(1976), 105-109. | Zbl | MR | Numdam

[62] C. Borell - Convexity in Gauss space, in : Aspects statistiques et aspects physiques des processus gaussiens (Colloques internationaux du CNRS), 1981, 27-37. | Zbl | MR

[63] P. A. Meyer - Démonstration probabiliste de certaines inégalités de Littlewood-Paley, Sém. Proba. X, Springer-Verlag, Lect. Notes in Math. 511(1976). | Zbl | Numdam

[64] N. Th. Varopoulos - Aspects of probabilistic Littlewood-Paley theory, J. Funct. Anal. 38(1980), 25-60. | Zbl | MR

[65] P. Malliavin - Stochastic Calculus of Variation and hypoelliptic operators, Proc. of Int. Symp. SDE (Kyoto 1976), Tokyo (1978). | Zbl | MR

[66] D. W. Stroock - The Malliavin Calculus and its Application to second order parabolic differential equations : Part I, Math. Systems Theory 14 (1981), 25-65. | Zbl | MR

[67] J. M. Bismut - Martingales, the Malliavin calculus and hypoellipticity under general Hörmander's conditions, Zeitschrift für Wahr. 56(1981), 469-505. | Zbl | MR

[68] A. V. Skorokhod - Integration in Hilbert space, Springer-Verlag, 1974. | Zbl | MR

[69] F. B. Knight - Essentials of brownian motion and diffusion, Amer. Math. Soc., Maths Surveys 18(1981). | Zbl | MR

[70] K. Itô, H. P. Mckean - Diffusion processes and their sample paths, Springer, 1965. | Zbl

[71] E. Perkins Local Time is a semi-martingale, Zeitschrift für Wahr. 60(1982), 79-117. | Zbl | MR

[72] K. L. Chung Excursions in Brownian motion, Ark. Math. 14(1976), 155-177. | Zbl | MR

[73] J. Azéma - Quelques applications de la théorie générale des processus I, Invent. Math. 18(1972), 293-336. | Zbl | MR

[74] R. Fefferman, R. F. Gundy, M. Silverstein, E. Stein - Inequalities for Ratios of Functionals of Harmonic Functions, à paraître. | Zbl