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.