TY  - BOOK
AU  - Svishchuk,A.V.
TI  - Inhomogeneous random evolutions and their applications
SN  - 9780429457548
AV  - HG106 
U1  - 515/.732 23
PY  - 2019///]
CY  - Boca Raton, FL
PB  - CRC Press, Taylor & Francis Group
KW  - Finance
KW  - Mathematical models
KW  - Insurance
KW  - Stochastic processes
KW  - Banach spaces
KW  - MATHEMATICS / General
KW  - bisacsh
KW  - MATHEMATICS / Probability & Statistics / General
KW  - MATHEMATICS / Probability & Statistics / Bayesian Analysis
N1  - Cover; Half Title; Title Page; Copyright Page; Dedication; Contents; Preface; Acknowledgments; Introduction; Part I: Stochastic Calculus in Banach Spaces; 1. Basics in Banach Spaces; 1.1 Random Elements, Processes and Integrals in Banach Spaces; 1.2 Weak Convergence in Banach Spaces; 1.3 Semigroups of Operators and Their Generators; Bibliography; 2. Stochastic Calculus in Separable Banach Spaces; 2.1 Stochastic Calculus for Integrals over Martingale Measures; 2.1.1 The Existence of Wiener Measure and Related Stochastic Equations; 2.1.2 Stochastic Integrals over Martingale Measures; 2.1.2.1 Orthogonal Martingale Measures2.1.2.2 Ito's Integrals over Martingale Measures; 2.1.2.3 Symmetric (Stratonovich) Integral over Martingale Measure; 2.1.2.4 Anticipating (Skorokhod) Integral over Martingale Measure; 2.1.2.5 Multiple Ito's Integral over Martingale Measure; 2.1.3 Stochastic Integral Equations over Martingale Measures; 2.1.4 Martingale Problems Associated with Stochastic Equations over Martingale Measures; 2.1.5 Evolutionary Operator Equations Driven by Wiener Martingale Measures; 2.2 Stochastic Calculus for Multiplicative Operator Functionals (MOF); 2.2.1 Definition of MOF2.2.2 Properties of the Characteristic Operator of MOF; 2.2.3 Resolvent and Potential for MOF; 2.2.4 Equations for Resolvent and Potential for MOF; 2.2.5 Analogue of Dynkin's Formulas (ADF) for MOF; 2.2.6 Analogue of Dynkin's Formulae (ADF) for SES; 2.2.6.1 ADF for Traffic Processes in Random Media; 2.2.6.2 ADF for Storage Processes in Random Media; 2.2.6.3 ADF for Diffusion Process in Random Media; Bibliography; 3. Convergence of Random Bounded Linear Operators in the Skorokhod Space; 3.1 Introduction; 3.2 D-Valued Random Variables and Various Propertieson Elements of D3.3 Almost Sure Convergence of D-Valued RandomVariables; 3.4 Weak Convergence of D-Valued Random Variables; Bibliography; Part II: Homogeneous and Inhomogeneous Random Evolutions; 4. Homogeneous Random Evolutions (HREs) and their Applications; 4.1 Random Evolutions; 4.1.1 Definition and Classification of Random Evolutions; 4.1.2 Some Examples of RE; 4.1.3 Martingale Characterization of Random Evolutions; 4.1.4 Analogue of Dynkin's Formula for RE (see Chapter 2); 4.1.5 Boundary Value Problems for RE (see Chapter 2); 4.2 Limit Theorems for Random Evolutions4.2.1 Weak Convergence of Random Evolutions (see Chapter 2 and 3); 4.2.2 Averaging of Random Evolutions; 4.2.3 Diffusion Approximation of Random Evolutions; 4.2.4 Averaging of Random Evolutions in Reducible Phase Space Merged Random Evolutions; 4.2.5 Diffusion Approximation of Random Evolutions in Reducible Phase Space; 4.2.6 Normal Deviations of Random Evolutions; 4.2.7 Rates of Convergence in the Limit Theorems for RE; Bibliography; 5. Inhomogeneous Random Evolutions (IHREs); 5.1 Propagators (Inhomogeneous Semigroup of Operators)
N2  - "The book deals with inhomogeneous REs and their applications, which are more general and more applicable because they describe in a much better way the evolutions of many processes in real world, which have no homogeneous evolution/behaviour, including economics, finance and insurance"--
UR  - https://www.taylorfrancis.com/books/9780429457548
UR  - http://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf
ER  -