Stochastic evolution equations in UMD Banach spaces
Let \(E\) be a UMD Banach space, \(H\) a Hilbert space, \(A\) the generator of a \(C_0\)-semigroup on \(E\), \(W_H\) a cylindrical Brownian motion on \(H\). Under Lipschitz and lineae growth conditions on \(F\) and \(B\), the existence, uniqueness and space-time regularity of solutions to the following semi-linear stochastic differential equation were addressed in the paper: \[ d U(t)= (AU(t)+F(t,U(t)))d t +B(t, U(t))d W_H(t). \]
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