
doi: 10.1007/bf01048965
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.
stochastic parabolic equations, Stochastic partial differential equations (aspects of stochastic analysis), One-parameter semigroups and linear evolution equations, General theory of partial differential operators, existence, uniqueness, PDEs with randomness, stochastic partial differential equations, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, space of initial conditions
stochastic parabolic equations, Stochastic partial differential equations (aspects of stochastic analysis), One-parameter semigroups and linear evolution equations, General theory of partial differential operators, existence, uniqueness, PDEs with randomness, stochastic partial differential equations, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, space of initial conditions
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