Stochastic partial differential equations in \(M\)-type 2 Banach spaces
The author proves an existence and uniqueness theorem for a stochastic differential equation in \(M\)-type 2 Banach spaces of the following type \[ du(t) + Au(t)dt = \sum B^j u(t) dw^j(t) + f(t), \quad u(0) = u_0, \] where \(- A\) is a generator of an analytic semigroup \(\{e^{- tA}\}_{r \geq 0}\) on \(X\), an \(M\)-type 2 Banach space, \(B^1, \ldots, B^d\) are linear operators in \(X\) and \(w(t)\) is a \(d\)-dimensional Wiener process. The author considers the case, when the space of initial conditions is some real interpolation space between the domain of \(A\) and \(X\), and the case, when the space of initial conditions is \(X\). Also the author considers the case, when \(X\) is a Hilbert space and applies the obtained results to stochastic parabolic equations.
scientific article; zbMATH DE number 723919
scientific article