In the present paper the stochastic Volterra equation in a separable Hilbert space
Where , , is a closed unbounded linear operator in with a dense domain , is a cylindrical Wiener process with covariance operator , is a linear bounded symmetric nonnegative operator in separable Hilbert space , is an -valued, -measurable random variable and is -predictable process such that
is set of all Hilbert-Schmidt operators from into .
An -valued predictable process , , is said to be a strong solution to (1), if has a version such that for almost all ; for any
and for any equation (1) holds .
Under certain assumptions the authors show that (1) has a strong solution. Precisely, the stochastic convolution
where is a resolvent determined by operator , is a strong solution to (1) with .