×

zbMATH — the first resource for mathematics

Integral of differential forms along the path of diffusion processes. (English) Zbl 0462.60056

MSC:
60H05 Stochastic integrals
58J65 Diffusion processes and stochastic analysis on manifolds
60G44 Martingales with continuous parameter
60D05 Geometric probability and stochastic geometry
60J65 Brownian motion
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bishop, R. L. and Crittenden, R. J., Geometry of manifolds, Academic Press, 1964. · Zbl 0132.16003
[2] Blumenthal, R. M. and Getoor, R. K., Markov processes and potential theory, Academic Press, 1968. · Zbl 0169.49204 · www.sciencedirect.com
[3] de Rham, G., Varietes differentiates, Hermann, 1960.
[4] Helgason, S., Differential geometry and symmetric spaces, Academic Press, 1962. · Zbl 0111.18101
[5] Ito, K., Stochastic differentials, Appl. Math. & Optimization, 1 (1975), 374-381. · Zbl 0325.60057 · doi:10.1007/BF01447959
[6] , Brownian motion on Riemannian manifold and harmonic tensor fields (in Japanese), Sugaku 28 (1976), 137-146.
[7] Ikeda, N. and Watanabe, S., Heat equation and diffusion on Riemannian manifold with boundary, Proc. of Symp. on SDE, Kyoto, (1976), 75-94. · Zbl 0451.60073
[8] Kunita, H. and Watanabe, S., On square integrable martingales, Nagoya Math. Jour., 30 (1967), 209-245. · Zbl 0167.46602
[9] Malliavin, P., Formules de la moyenne calcul de perturbations el theoremes d’annulation pour les formes harmomques, Jour. Funct. Anal., 17 (1974), 274-291. · Zbl 0425.58022 · doi:10.1016/0022-1236(74)90041-X
[10] Milnor, J., Morse theory, Annals of Math. Studies, 51, Princeton Univ. Press, 1963. · Zbl 0108.10401
[11] Motoo, M. and Watanabe, S., On a class of additive functionals of Markov processes, Jour. Math. Kyoto Univ. 4 (1965), 429-469. · Zbl 0137.11703
[12] Nakao, S. and Yamato, Y., Approximation theorem on stochastic differential equations, Proc. of Symp. on SDE, Kyoto, (1976), 283-296. · Zbl 0443.60051
[13] Nelson, E., The adjoint Markoff process, Duke Math. Jour. 25 (1958), 671-690. · Zbl 0084.13402 · doi:10.1215/S0012-7094-58-02561-4
[14] Skorobod, A. V., Additive functionals of a process of Brownian motion, Theory Prob. & Appl. 6 (1961), 396-404. · Zbl 0114.33602 · doi:10.1137/1106052
[15] Tanaka, H., Note on continuous additive functionals of a 1-dimensional Brownian path, Z. Wahr. 1 (1963), 251-257. · Zbl 0129.30701 · doi:10.1007/BF00532497
[16] Wentzell, A. D., Nonnegative additive functionals of Markov processes, Soviet Math. Dokl., 2 (1961), 218-221.
[17] , On continuous additive functionals of a multidimensional Wiener process, Soviet Math. Dokl., 3 (1962), 246-267. · Zbl 0126.13801
[18] Yor, M., Formule de Cauchy relative a certains lacets browniens, Bull. Soc. Math. France, 105 (1977), 3-31. · Zbl 0375.60068 · numdam:BSMF_1977__105__3_0 · eudml:87309
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.