國立虎尾科技大學 |

Stochastic integration in Banach spaces = theory and applications /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Stochastic integration in Banach spaces/ by Vidyadhar Mandrekar, Barbara Rudiger.
Reminder of title:	theory and applications /
Author:	Mandrekar, Vidyadhar.
other author:	Rudiger, Barbara.
Published:	Cham :Springer International Publishing : : 2015.,
Description:	viii, 211 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Banach spaces. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-12853-5
ISBN:	9783319128535 (electronic bk.)

Stochastic integration in Banach spaces = theory and applications /
Mandrekar, Vidyadhar.

Stochastic integration in Banach spacestheory and applications /[electronic resource] :by Vidyadhar Mandrekar, Barbara Rudiger. - Cham :Springer International Publishing :2015. - viii, 211 p. :ill., digital ;24 cm. - Probability theory and stochastic modelling,v.732199-3130 ;. - Probability theory and stochastic modelling ;v.72..

1.Introduction -- 2.Preliminaries -- 3.Stochastic Integrals with Respect to Compensated Poisson Random Measures -- 4.Stochastic Integral Equations in Banach Spaces -- 5.Stochastic Partial Differential Equations in Hilbert Spaces -- 6.Applications -- 7.Stability Theory for Stochastic Semilinear Equations -- A -- Some Results on compensated Poisson random measures and stochastic integrals -- References -- Index.

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.

ISBN: 9783319128535 (electronic bk.)

Standard No.: 10.1007/978-3-319-12853-5doiSubjects--Topical Terms:

676255
Banach spaces.

LC Class. No.: QA322.2

Dewey Class. No.: 515.732

Stochastic integration in Banach spaces = theory and applications /
LDR:02854nam a2200337 a 4500 001 835738
003 DE-He213
005 20150812135713.0
006 m d
007 cr nn 008maaau
008 160421s2015 gw s 0 eng d
020 $a 9783319128535 (electronic bk.)
020 $a 9783319128528 (paper)
024 7 $a 10.1007/978-3-319-12853-5 $2 doi
035 $a 978-3-319-12853-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA322.2
072 7 $a PBT $2 bicssc
072 7 $a PBWL $2 bicssc
072 7 $a MAT029000 $2 bisacsh
082 0 4 $a 515.732 $2 23
090 $a QA322.2 $b .M273 2015
100 1 $a Mandrekar, Vidyadhar. $3 783159
245 1 0 $a Stochastic integration in Banach spaces $h [electronic resource] : $b theory and applications / $c by Vidyadhar Mandrekar, Barbara Rudiger.
260 $a Cham : $c 2015. $b Springer International Publishing : $b Imprint: Springer,
300 $a viii, 211 p. : $b ill., digital ; $c 24 cm.
490 1 $a Probability theory and stochastic modelling, $x 2199-3130 ; $v v.73
505 0 $a 1.Introduction -- 2.Preliminaries -- 3.Stochastic Integrals with Respect to Compensated Poisson Random Measures -- 4.Stochastic Integral Equations in Banach Spaces -- 5.Stochastic Partial Differential Equations in Hilbert Spaces -- 6.Applications -- 7.Stability Theory for Stochastic Semilinear Equations -- A -- Some Results on compensated Poisson random measures and stochastic integrals -- References -- Index.
520 $a 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.
650 0 $a Banach spaces. $3 676255
650 0 $a Stochastic processes. $3 528256
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Probability Theory and Stochastic Processes. $3 593945
650 2 4 $a Quantitative Finance. $3 669372
650 2 4 $a Partial Differential Equations. $3 671119
700 1 $a Rudiger, Barbara. $3 1065272
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Probability theory and stochastic modelling ; $v v.72. $3 1064457
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-12853-5
950 $a Mathematics and Statistics (Springer-11649)