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Itô’s- and Tanaka’s-type formulae for the stochastic heat equation: The linear case. (English) Zbl 1084.60039
The authors study the stochastic heat equation with additive noise in dimension one, that is, $$dX_t = \Delta X_t dt + dW_t,$$ $$t \in (0,T], X_0=0$$, where $$W$$ denotes a cylindrical Brownian motion. They understand the solution of such equation in a mild sense and can be solved explicitly in the form of a stochastic convolution. Using the representation of the solution given by the convolution of $$W$$ by the operator-valued kernel $$e^{(t-s)\Delta}$$, the authors obtain Itô’s and Tanaka’s type formulae associated to $$X$$. In order to obtain these results, they adapt the methodology used to study some properties of fractional Brownian motion to their infinite-dimensional case.

##### MSC:
 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 60H05 Stochastic integrals 60H07 Stochastic calculus of variations and the Malliavin calculus 60G15 Gaussian processes
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##### References:
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