Ito formula in nuclear Fréchet space
Let H be a separable Hilbert space, X be a nuclear Fréchet space, E be a separable Banach space with BAP, W(t) be a Wiener process in E such that W(1) has the covariance operator \(jj^*\), where j:\(H\to E\) is the continuous linear injection. For each \(A\in L(H,X)\) the random element AW(t) can be uniquely defined. L(H,X) with the topology of uniform convergence on bounded subsets of H is a separable Fréchet space. The stochastic integral is defined for adapted to W(t) strong second order random functions A:[0,T]\(\times \Omega \to L(H,X)\) (with respect to W(t)) and an analogue of Ito's formula is obtained. Reviewer's remark: \textit{B. I. Mamporiya} [Soobshch. Akad. Nauk Gruz. SSR 105, 501-504 (1982; Zbl 0491.60051)] has defined the stochastic integral for random functions A:[0,T]\(\times \Omega \to L(E,Y)\), where Y is a Banach space, but his definition is valid also when Y is a Fréchet space.
scientific article; zbMATH DE number 3862115