Considering Poisson random measures as the driving sources for stochastic (partial)
differential equations allows us to incorporate jumps and to model sudden unexpected
phenomena. By using such equations the present book introduces a new method for modeling the
states of complex systems perturbed by random sources over time such as interest rates in
financial markets or temperature distributions in a specific region. It studies properties of
the solutions of the stochastic equations observing the long-term behavior and the sensitivity
of the solutions to changes in the initial data. The authors consider an integration theory of
measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case
whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book
is intended for graduate students and researchers in stochastic (partial) differential
equations mathematical finance and non-linear filtering and assumes a knowledge of the
required integration theory existence and uniqueness results and stability theory. The results
will be of particular interest to natural scientists and the finance community. Readers should
ideally be familiar with stochastic processes and probability theory in general as well as
functional analysis and in particular the theory of operator semigroups.
