Abstract
We prove a generalization of Bismut-Itô-Kunita formula to infinite dimensions and derive an uniqueness result for Wiener space valued processes which holds for a special class of Bernstein processes.
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Kunita, H.: Some Extensions of It ô 's Formula, Lecture Notes in Mathematics 850, SpringerVerlag, Berlin, 1981, pp. 118-141.
Bismut, J. M.: A generalized formula of It ô and some other properties of stochastic flows, Z.W. 55(1981), 331-350.
Albeverio, S. and R¨ockner, M.: ‘Dirichlet form methods for uniqueness of martingale problems and applications’, Proc.Symposium in Pure Mathematics 57, Stochastic Analysis American Mathematical Society, 1995, pp. 513-527.
Peters, G.: ‘Anticipating flows on the Wiener space generated by vector fields of low regularity’, J.Funct.Anal. 142(1996), 129-192.
Kusuoka, S.: ‘The nonlinear transformation of Gaussian measure, on Banach space and its absolute continuity’, J.Fac.Sci., Univ.Tokyo 29(1982), 567-598.
Malliavin, P.: Stochastic calculus of variations and hypoelliptic operators, in 'Proc. of International Symposium on Stochastic Differential Equations, Kyoto' (K. Itô , ed.), Kinokuniya-Wiley, Tokyo, 1978.
Korezlioglu, H. and Ñstünel, A. S.: ‘Une formule d'Itô sur les espaces de Wiener abstraits’, C. R.Acad.Sc.Paris 303(1986), 247-249.
Cruzeiro, A.B.: ‘équations différentielles sur l'espace deWiener et formules de Cameron-Martin nonlin éaires’, J.Funct.Anal. 54(1983), 206-227.
Malliavin, P.: Implicit functions in finite corank on theWiener space, in 'Tanniguchi, Symposium 1992’, Kinokuniya, Tokyo, 1994.
Cruzeiro, A. B. and Zambrini, J. C.: ‘Malliavin calculus and Euclidean quantum mechanics. I. Variational principle for infinite dimensional processes’, J.Funct.Anal. 130(1995), 450-476.
Cruzeiro, A. B. and Zambrini, J. C.: Ornstein-Uhlenbeck processes as Bernstein processes, in 'Barcelona Seminar on Stochastic Analysis' (Nualart and M. Sanz-Solé, eds.), Progress in Physics 32, Birkhäuser, 1993, pp. 40-61.
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Oliveira, M.J. An Uniqueness Result for a Class of Wiener-Space Valued Stochastic Differential Equations. Potential Analysis 11, 77–99 (1999). https://doi.org/10.1023/A:1008655728739
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DOI: https://doi.org/10.1023/A:1008655728739