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Stochastic convolution in separable Banach spaces and the stochastic linear Cauchy problem

Stochastic convolution in separable Banach spaces and the stochastic linear Cauchy problem

Let H be a separable real Hilbert space and let E be a separable real Banach space. We develop a general theory of stochastic convolution of ℒ(H,E)-valued functions with respect to a cylindrical Wiener process ${W_{t}^{H}}_{t ∈ [0,T]}$ with Cameron-Martin