Abstract
The aim of this paper is to present some versions of the Stroock and Varadhan support theorem [SV] in infinite dimensions. First, a theorem on the support for some stochastic nonlinear partial differential equations is examined We consider a model similar to that in [Pa] and [Tw1]. Second, the support theorem for the stochastic Navier-Stokes equations is given. We consider a model similar to that in [Tw2]. In the proofs of our support theorems we generalize the method of Mackevičius [Ma] and Gyöngy [Gy] to our infinite-dimensional models. In this aim we also prove some modified versions of the approximation theorems of Wong-Zakai type investigated in [Tw1] and [Tw2], respectively.
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References
M. Capiński and N. Cutland, Stochastic Navier-Stokes equations, Acta Applicandae Math. 25 (1991), 59–85.
F. Flandoli and D. Ggtarek, Martingale and stationary solutions for stochastic Navier-Stokes equations. Preprints di Matematica No. 14. Scuola Normale Superiore Pisa, 1994, 1–33.
I. Gyöngy, The stability of stochastic partial differential equations and applications. Theorems on supports, in: Lecture Notes Math. 1390, Springer, Berlin, 1989, 91–118.
N.Ikeda and S.Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981.
N.U. Krylov and B.L. Rozovskii, On stochastic evolution equations. Itogi Nauki i Techniki. Teor. Veroyatnost. Moscow, 14 (1979), 71–146.
V. Mackevičius, On the support of a solution of stochastic differential equations, Liet. Mat. Rink. 26(1) (1986), 91–98 (in Russian).
E.Pardoux, Equations aux dérivées partielles stochastiques non linéaires monotones. Thèse. Univ. Paris Sud, 1975.
D.W. Stroock and S.R.S. Varadhan, On the support of diffusion processes with applications to the strong maximum principle, in: Proc. 6th Berkeley Sympos. Math. Statist. Probab. III Univ. California Press, Berkeley, 1972, 333–359.
K. Twardowska, An approximation theorem of Wong-Zakai type for nonlinear stochastic partial differential equations, Stochastic Anal. Appl. 13(5), (1995), 601–626.
K. Twardowska, An approximation theorem of Wong-Zakai type for stochastic Navier-Stokes equations, Rend. Sem. Math. Univ. Padova 96 (1996), 15–36.
K. Twardowska, Wong-Zakai approximations for stochastic differential equations, Acta Applicandae Math. 43, (1996), 317–359.
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Twardowska, K. (1997). On Support Theorems for Stochastic Nonlinear Partial Differential Equations. In: Stochastic Differential and Difference Equations. Progress in Systems and Control Theory, vol 23. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1980-4_24
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DOI: https://doi.org/10.1007/978-1-4612-1980-4_24
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7365-3
Online ISBN: 978-1-4612-1980-4
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