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Set-Valued Stochastic Integrals and Applications

✍ Scribed by Michał Kisielewicz

Publisher
Springer International Publishing;Springer
Year
2020
Tongue
English
Leaves
287
Series
Springer Optimization and Its Applications 157
Edition
1st ed.
Category
Library
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✦ Synopsis

This book is among the first concise presentations of the set-valued stochastic integration theory as well as its natural applications, as well as the first to contain complex approach theory of set-valued stochastic integrals. Taking particular consideration of set-valued Itô , set-valued stochastic Lebesgue, and stochastic Aumann integrals, the volume is divided into nine parts. It begins with preliminaries of mathematical methods that are then applied in later chapters containing the main results and some of their applications, and contains many new problems. Methods applied in the book are mainly based on functional analysis, theory of probability processes, and theory of set-valued mappings.
The volume will appeal to students of mathematics, economics, and engineering, as well as to mathematics professionals interested in applications of the theory of set-valued stochastic integrals.

✦ Table of Contents

Front Matter ....Pages i-xii
Preliminaries (Michał Kisielewicz)....Pages 1-59
Multifunctions (Michał Kisielewicz)....Pages 61-79
Decomposable Subsets of ({\mathbb {L}}^p(T,\mathcal {F},\mu ,X)) (Michał Kisielewicz)....Pages 81-106
Aumann Stochastic Integrals (Michał Kisielewicz)....Pages 107-139
Itô Set-Valued Integrals (Michał Kisielewicz)....Pages 141-193
Stochastic Differential Inclusions (Michał Kisielewicz)....Pages 195-210
Set-Valued Stochastic Equations and Inclusions (Michał Kisielewicz)....Pages 211-247
Stochastic Optimal Control Problems (Michał Kisielewicz)....Pages 249-258
Mathematical Finance Problems (Michał Kisielewicz)....Pages 259-274
Back Matter ....Pages 275-281

✦ Subjects

Mathematics; Probability Theory and Stochastic Processes; Operator Theory; Measure and Integration

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