Ito's- and Tanaka's-type formulae for the stochastic heat equation: The linear case |
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| Authors: | Mihai Gradinaru Ivan Nourdin |
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| Institution: | Université Henri Poincaré, Institut de Mathématiques Élie Cartan, B.P. 239, F - 54506 Vandœuvre-lès-Nancy Cedex, France |
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| Abstract: | In this paper, we consider the linear stochastic heat equation with additive noise in dimension one. Then, using the representation of its solution X as a stochastic convolution of the cylindrical Brownian motion with respect to an operator-valued kernel, we derive Itô's- and Tanaka's-type formulae associated to X. |
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| Keywords: | 60H15 60H05 60H07 60G15 |
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