The calculus of boundary processes
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 17 (1984) no. 4, pp. 507-622.
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     year = {1984},
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     url = {http://archive.numdam.org/articles/10.24033/asens.1482/}
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Bismut, Jean-Michel. The calculus of boundary processes. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 17 (1984) no. 4, pp. 507-622. doi : 10.24033/asens.1482. http://archive.numdam.org/articles/10.24033/asens.1482/

[1] V. Arnold, Méthodes mathématiques de la mécanique classique, Moscou, Ed. MIR, 1976. | MR | Zbl

[2] J. Azéma and T. Jeulin, Précisions sur la mesure de Föllmer (Ann. Inst. H.-Poincaré, section B, Vol. 12, 1976, pp. 257-283). | Numdam | MR | Zbl

[3] M. Barlow, Study of a Filtration Expanded to Include an Honest Time (Z. Warsch., Vol. 44, 1978, pp. 307-323). | MR | Zbl

[4] P. Billingsley, Convergence of Probability Measures, New York, Wiley, 1978. | Zbl

[5] J. M. Bismut, Mécanique aléatoire (Lecture Notes in Math., No. 866, Berlin, Springer, 1981). | MR | Zbl

[6] J. M. Bismut, A Generalized Formula of Ito and Some Other Properties of Stochastic Flows (Z. Wahrsch., Vol. 55, 1981, pp. 331-350). | MR | Zbl

[7] J. M. Bismut, Martingales, the Malliavin Calculus and Hypoellipticity Under General Hörmander's Conditions (Z. Wahrsch., Vol. 56, 1981, pp. 469-505). | MR | Zbl

[8] J. M. Bismut, Calcul des variations stochastiques et processus de sauts (Z. Wahrsch., Vol. 63, 1983, pp. 147-235). | MR | Zbl

[9] J. M. Bismut, Calcul des variations sur les processus de sauts (C.R. Acad. Sc., Paris, T. 293, série I, 1981, pp. 565-568). | MR | Zbl

[10] J. M. Bismut and D. Michel, Diffusions conditionnelles (J. Funct. Anal.. Part I, Vol. 44, 1981, pp. 174-211. Part II, Vol. 45, 1982, pp. 274-292). | MR | Zbl

[11] C. Dellacherie and P. A. Meyer, Probabilités et potentiels, Chap. I-IV, Hermann, Paris, 1975. Chap. V-VIII, Hermann, Paris, 1980. | Zbl

[12] H. Doss, Liens entre équations différentielles stochastiques et ordinaires (Ann. Inst. H.-Poincaré, section B, Vol. 13, 1977, pp. 99-125). | EuDML | Numdam | MR | Zbl

[13] H. Föllmer, The Exit Measure of a Supermartingale (Z. Wahrsch., Vol. 21, 1972, pp. 154-166). | MR | Zbl

[14] U. Haussmann, On the Integral Representation of Ito Processes (Stochastics, Vol. 3, 1979, pp. 17-27). | MR | Zbl

[15] L. Hörmander, Hypoelliptic Second Order Differential Equations (Acta Math., Vol. 117, 1967, pp. 147-171). | MR | Zbl

[16] N. Ikeda, On the Construction of Two-Dimensional Diffusion Processes Satisfying Wentzell's Boundary Conditions and Its Application to Boundary Value Problems (Mem. Coll. Sc. Univ. Kyoto Math., Vol. 33, 1961, pp. 367-427). | MR | Zbl

[17] N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, Amsterdam, North-Holland, 1981. | MR | Zbl

[18] K. Itô and H. P. Mckean Jr., Diffusion Processes and Their Sample Paths (Grundlehren Math. Wissenschaften, Band 125, Berlin, Springer, 1974). | MR | Zbl

[19] J. Jacod, Calcul stochastique et problème des martingales (Lecture Notes in Math., No. 714, Berlin, Springer, 1979). | MR | Zbl

[20] J. Jacod and M. Yor, Étude des solutions extrémales et représentation intégrale des solutions pour certains problèmes de martingales (Z. Wahrsch., Vol. 38, 1977, pp. 83-125). | MR | Zbl

[21] T. Jeulin, Semi-martingales et grossissement d'une filtration (Lectures Notes in Math., No. 833, Berlin, Springer, 1980). | MR | Zbl

[22] T. Jeulin and M. Yor, Sur les distributions de certaines fonctionnelles du mouvement brownien (Séminaire de Probabilités, No. XV, pp. 210-226, Lectures Notes in Math., No. 850, Berlin, Springer, 1981). | EuDML | Numdam | MR | Zbl

[23] T. Jeulin and M. Yor, Grossissement d'une filtration et semi-martingales : formules explicites (Séminaire de Probabilités, No. XII, pp. 78-97, Lecture Notes in Math., No. 649, Berlin, Springer, 1978). | EuDML | Numdam | MR | Zbl

[24] J. J. Kohn, Pseudo-Differential Operators and Hypoellipticity (Proc. Symp. Pure Math., Vol. 23, 1973, pp. 61-69). | MR | Zbl

[25] H. Kunita, On the Decomposition of Solutions of Stochastic Differential Equations, in : Stochastic Integrals, D. WILLIAMS, Ed., pp. 213-255 (Lecture Notes in Math., No. 851, Berlin, Springer, 1981). | MR | Zbl

[26] S. Kusuoka and D. Stroock, Applications of the Malliavin Calculus, Part I, Proceedings of the Katata Conference in Probability, 1982 (to appear). | Zbl

[27] B. Maisonneuve, Systèmes régénératifs, Société mathématique de France, Astérisque, No. 15, 1974. | Numdam | MR | Zbl

[28] B. Maisonneuve and P. A. Meyer, Ensembles aléatoires markoviens homogènes (Séminaire de Probabilités, No. VIII, pp. 172-261, Lecture Notes in Math., No. 381, Berlin, Springer, 1974). | EuDML | Numdam | Zbl

[29] P. Malliavin, Stochastic Calculus of Variations and Hypoelliptic Operators, in : Proceedings of the Conference on Stochastic Differential Equations of Kyoto, 1976, K. ITÔ, Ed., pp. 155-263, Tokyo, Kinokuniya and New York, Wiley, 1978. | Zbl

[30] P. Malliavin, Ck Hypoellipticity with Degeneracy, in : Stochastic Analysis, pp. 199-214, A. FRIEDMAN and M. PINSKY, Ed., New York, Acad. Press, 1978. | MR | Zbl

[31] P. A. Meyer, Un cours sur les intégrales stochastiques (Séminaire de Probabilités, No. X, pp. 245-400 (Lectures Notes in Math., No. 511, Berlin, Springer, 1973). | EuDML | Numdam | MR | Zbl

[32] P. A. Meyer, Flot d'une équation différentielle stochastique (Séminaire de Probabilités, No. XV, pp. 103-117 (Lecture Notes in Math., No. 850, Berlin, Springer, 1981). | EuDML | Numdam | MR | Zbl

[33] L. C. G. Rogers, Williams Characterization of the Brownian Excursion Law : Proof and Applications (Séminaire de Probabilités, No. XV, pp. 227-250, Lecture Notes in Math., No. 850, Berlin, Springer, 1981). | EuDML | Numdam | MR | Zbl

[34] I. Shigekawa, Derivatives of Wiener Functionals and Absolute Continuity of Induced Measures (J. Math. Kyoto Univ., Vol. 20, 1980, pp. 263-289). | MR | Zbl

[35] D. Stroock, Diffusion Processes Associated with Lévy Generators (Z. Wahrsch., Vol. 32, 1975, pp. 209-244). | MR | Zbl

[36] D. Stroock, The Malliavin Calculus and its Applications to Second-Order Parabolic Differential Equations (Math. Syst. Theory., Part. I, Vol. 14, 1981, pp. 25-65. Part II : Vol. 14, 1981, pp. 141-171). | MR | Zbl

[37] D. Stroock, The Malliavin Calculus : a Functional Analytic Approach (J. Funct. Anal., Vol. 44, 1981, pp. 212-257). | MR | Zbl

[38] D. Stroock, Some Applications of Stochastic Calculus to Partial Differential Equations [Cours de Probabilité de Saint-Flour], Lecture Notes in Math., No. 976, pp. 267-382, Berlin, Springer, 1983. | MR | Zbl

[39] D. Stroock and S. R. S. Varadhan, Diffusion Processes with Boundary Conditions (Comm. Pure Appl. Math., Vol. 24, 1971, pp. 147-225). | MR | Zbl

[40] D. Stroock and S. R. S. Varadhan, Multidimensional Diffusion Processes (Grundlehren Math. Wissenschaften, Band 233, Berlin, Springer, 1979). | MR | Zbl

[41] H. Sussmann, On the Gap Between Deterministic and Stochastic Ordinary Differential Equations (Ann. Prob., Vol. 6, 1978, pp. 19-41). | MR | Zbl

[42] F. Treves, Introduction to Pseudodifferential Operators and Fourier Integral Operators, Vol. 1, New York, Plenum Press, 1981. | MR | Zbl

[43] S. Watanabe, On Stochastic Differential Equations for Multidimensional Diffusion Processes with Boundary Conditions (J. Math. Kyoto Univ.. Part I : Vol. 11, 1971, pp. 169-180. Part II : Vol. 11, 1971, pp. 545-551). | MR | Zbl

[44] S. Watanabe, Excursion Point Process of Diffusion and Stochastic Integral, in : Proceedings of the International Conference on Stochastic Differential Equations of Kyoto, 1976, K. ITÔ, Ed., pp. 437-461, Tokyo, Kinokuniya and New York, Wiley, 1978. | MR | Zbl

[45] D. Williams, Path. Decomposition and Continuity of Local Time for One-Dimensional Diffusions (Proc. London Math. Society, Ser. 3, Vol. 28, 1974, pp. 738-768). | MR | Zbl

[46] D. Williams, Diffusions, Markov Processes and Martingales, Vol. 1, Foundations, New York, Wiley, 1979. | MR | Zbl

[47] D. Williams, To Begin at the Beginning, in : Stochastic Integrals, D. WILLIAMS, Ed., pp. 1-55 (Lecture Notes in Math., No. 851, Berlin, Springer, 1981). | MR | Zbl

[48] M. Yor, Grossissement d'une filtration et semi-martingales : théorèmes généraux (Séminaire de Probabilités, No. XII, pp. 61-69, Lecture Notes in Math., No. 649, Berlin, Springer, 1978). | EuDML | Numdam | MR | Zbl

[49] M. Yor, Sur le balayage des semi-martingales continues (Séminaire de Probabilités, No. XIII, pp. 453-471, Lecture Notes in Math., No. 721, Berlin, Springer, 1979). | EuDML | Numdam | MR | Zbl

[50] J. M. Bismut, Jump Processes and Boundary Processes [Proceedings of the Katata Conference in Probability, 1982 (to appear)]. | MR | Zbl

[51] J. M. Bismut, On the Set of Zeros of Certain Semi-Martingales [Proc. London Math. Soc. (to appear)]. | MR | Zbl

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