Helmes, K.; Schwane, A. Levy’s stochastic area formula in higher dimensions. (English) Zbl 0522.60082 J. Funct. Anal. 54, 177-192 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 Documents MSC: 60J60 Diffusion processes 60J25 Continuous-time Markov processes on general state spaces 60J65 Brownian motion 58J65 Diffusion processes and stochastic analysis on manifolds 65H10 Numerical computation of solutions to systems of equations 60H15 Stochastic partial differential equations (aspects of stochastic analysis) Keywords:stochastic area process; Heisenberg group; hypoelliptic operators; Girsanov formula PDFBibTeX XMLCite \textit{K. Helmes} and \textit{A. Schwane}, J. Funct. Anal. 54, 177--192 (1983; Zbl 0522.60082) Full Text: DOI References: [1] Breiman, L., Probability (1968), Addison-Wesley: Addison-Wesley New York · Zbl 0174.48801 [2] Cygan, J., Heat kernels for class 2 nilpotent groups, Studia Math., 64, 227-238 (1979) · Zbl 0336.35029 [3] Friedman, A., (Stochastic Differential Equations and Applications, Vol. 1,Vol. 2 (1976), Academic Press: Academic Press New York) [4] Gaveau, B., Principe de moindre action, propagation de la chaleur et estimées sous elliptiques sur certains groupes nilpotents, Acta Math., 139, 95-153 (1977) · Zbl 0366.22010 [5] Hulanicki, A., The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group, Studia Math., 56, 165-173 (1976) · Zbl 0336.22007 [6] Ikeda, N.; Watanabe, S., Stochastic Differential Equations and Diffusion Processes (1981), North-Holland: North-Holland Amsterdam · Zbl 0495.60005 [7] Kaplan, A., Fundamental solutions for a class of hypoelliptic pde generated by composition of quadratic forms, Trans. Amer. Math. Soc., 258, 147-153 (1980) · Zbl 0393.35015 [8] Lévy, P., Le mouvement Brownien plan, Amer. J. Math., 62, 487-550 (1940) · JFM 66.0619.02 [9] Lévy, P., Processus stochastiques et mouvement Brownien (1948), Gauthier-Villars: Gauthier-Villars Paris · Zbl 0034.22603 [10] Lévy, P., Calcul des probabilités—fonctions aléatoires Laplaciennes, C. R. Acad. Sci. Paris Ser. A-B, 229, 1057-1058 (1949) · Zbl 0035.08003 [11] Lévy, P., Errata, C. R. Acad. Sci. Paris Ser. A-B, 230, 689 (1950) [12] Lévy, P., Wiener’s random functions, and other Laplacian random functions, (Proceedings 2nd Berkeley Symp. (1951)) · Zbl 0044.13802 [13] Liptser, R.; Shiryayev, A., (Statistics of random processes, Vol. 1,Vol. 2 (1977), Springer-Verlag: Springer-Verlag New York) · Zbl 0364.60004 [14] Stroock, D.; Varadhan, S., Multidimensional diffusion processes (1979), Springer-Verlag: Springer-Verlag New York · Zbl 0426.60069 [15] Williams, D., On a stopped Brownian motion formula of H. M. Taylor, (Séminaire de Probabilités X. Séminaire de Probabilités X, Lect. Notes in Maths. 511 (1976), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0368.60056 [16] Yor, M., Remarques sur une formule de Paul Lévy, (Séminaire de Probabilités XIV. Séminaire de Probabilités XIV, Lect. Notes in Maths. 784 (1980), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0429.60045 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.