  We develop a theory of Hilbert-space valued stochastic integration with
respect to cylindrical martingale-valued measures. As part of our construction,
we expand the concept of quadratic variation introduced by Veraar and
Yaroslavtsev (2016) to the cylindrical martingale-valued measures, which are
allowed to have discontinuous paths (this is carried out within the context of
separable Banach spaces). Our theory of stochastic integration is applied to
the study of existence and uniqueness to stochastic partial differential
equations in Hilbert spaces.
