|
Showing 1 - 4 of
4 matches in All Departments
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.
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.
The systematic study of existence, uniqueness, and properties of
solutions to stochastic differential equations in infinite
dimensions arising from practical problems characterizes this
volume that is intended for graduate students and for pure and
applied mathematicians, physicists, engineers, professionals
working with mathematical models of finance. Major methods include
compactness, coercivity, monotonicity, in a variety of set-ups. The
authors emphasize the fundamental work of Gikhman and Skorokhod on
the existence and uniqueness of solutions to stochastic
differential equations and present its extension to infinite
dimension. They also generalize the work of Khasminskii on
stability and stationary distributions of solutions. New results,
applications, and examples of stochastic partial differential
equations are included. This clear and detailed presentation gives
the basics of the infinite dimensional version of the classic books
of Gikhman and Skorokhod and of Khasminskii in one concise volume
that covers the main topics in infinite dimensional stochastic
PDE's. By appropriate selection of material, the volume can be
adapted for a 1- or 2-semester course, and can prepare the reader
for research in this rapidly expanding area.
The systematic study of existence, uniqueness, and properties of
solutions to stochastic differential equations in infinite
dimensions arising from practical problems characterizes this
volume that is intended for graduate students and for pure and
applied mathematicians, physicists, engineers, professionals
working with mathematical models of finance. Major methods include
compactness, coercivity, monotonicity, in a variety of set-ups. The
authors emphasize the fundamental work of Gikhman and Skorokhod on
the existence and uniqueness of solutions to stochastic
differential equations and present its extension to infinite
dimension. They also generalize the work of Khasminskii on
stability and stationary distributions of solutions. New results,
applications, and examples of stochastic partial differential
equations are included. This clear and detailed presentation gives
the basics of the infinite dimensional version of the classic books
of Gikhman and Skorokhod and of Khasminskii in one concise volume
that covers the main topics in infinite dimensional stochastic
PDE's. By appropriate selection of material, the volume can be
adapted for a 1- or 2-semester course, and can prepare the reader
for research in this rapidly expanding area.
|
|