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Mikulevicius, R.

On the Cauchy problem for parabolic SPDEs in Hölder classes. (English) Zbl 1044.60050

Ann. Probab. 28, No. 1, 74-103 (2000).
Summary: We study Cauchy’s problem for certain second-order linear parabolic stochastic differential equation (SPDE) driven by a cylindrical Brownian motion. Considering its solution as a function with values in a probability space and using the methods of deterministic partial differential equations, we establish the existence and uniqueness of a strong solution in Hölder classes.

Cited in 2 Reviews
Cited in 18 Documents

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)

Keywords:

parabolic stochastic partial differential equations; Cauchy problem
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\textit{R. Mikulevicius}, Ann. Probab. 28, No. 1, 74--103 (2000; Zbl 1044.60050)
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