A stochastic convolution is a stochastic process of the form
Here
and
are Hilbert spaces,
is a strongly continuous semigroup
of bounded linear operators on
,
is a
-valued Wiener process, and
is a predictable stochastic process of suitable
linear operators from
to
for which the stochastic
integral exists. It gives the random forcing term in the integral formulation
of a stochastic differential equation on
.