Asymptotic analysis of unstable solutions of stochastic differential equations. (2020)

• Record Type: Book
• Further Information: Note: Grigorij Kulinich, Svitlana Kushnirenko, Yuliya Mishura.
• Other Names: Kulinich, Grigorij; Kushnirenko, Svitlana; Mishura, I︠U︡lii︠a︡ S
• Contents: Intro -- Preface -- Contents -- About the Authors -- Acronyms -- Abbreviations -- Notation -- 1 Introduction to Unstable Processes and Their Asymptotic Behavior -- 1.1 Equation with the Unit Diffusion Coefficient -- 1.1.1 Description and Motivation of the Model -- 1.1.2 Asymptotic Growth and Normalizing Multipliers for the Solutions -- 1.1.3 Bilayer Environment and Transition Density of the Limit Homogeneous Markov Process -- 1.1.4 Comparison with the Smooth Disturbing Process -- 1.1.5 Spatial Averaging of the Vibrational Type Coefficient -- 1.1.6 Functionals of the Solution 1.2 Equation with the Non-unit Diffusion Coefficient -- 2 Convergence of Unstable Solutions of SDEs to Homogeneous Markov Processes with Discontinuous Transition Density -- 2.1 Preliminaries -- 2.2 Necessary and Sufficient Conditions for the Weak Convergence of Solutions of SDEs to a Brownian Motion in a Bilayer Environment -- 2.3 Necessary and Sufficient Conditions for the Weak Convergence of Solutions of SDEs to a Process of Skew Brownian Motion Type -- 2.4 Examples -- 3 Asymptotic Analysis of Equations with Ergodic and Stochastically Unstable Solutions 3.1 Criteria of Instability and Ergodicity for the Solutions -- 3.2 Convergence of Normalized Stochastically Unstable Solutions to the Bessel Diffusion Process -- 3.3 Influence of the Coefficients of the Equation on the Limit Behavior of the Solutions -- 3.4 Influence of the Diffusion Coefficient on the Limit Behavior of the Solutions -- 3.5 Examples -- 4 Asymptotic Behavior of Integral Functionals of Stochastically Unstable Solutions -- 4.1 Weak Convergence to the Functionals of a Brownian Motion in a Bilayer Environment -- 4.2 Weak Convergence to the Functionals of the Bessel Diffusion Process 4.3 Results About Weak Convergence of the Mixed Functionals -- 4.4 Examples -- 5 Asymptotic Behavior of Homogeneous Additive Functionals Defined on the Solutions of Itô SDEs with Non-regular Dependence on a Parameter -- 5.1 Preliminaries -- 5.2 Theorem Concerning the Weak Compactness -- 5.3 Weak Convergence to the Solutions of Itô SDEs -- 5.4 Asymptotic Behavior of Integral Functionals of the Lebesgue Integral Type -- 5.5 Asymptotic Behavior of Integral Functionals of Martingale Type -- 5.6 Weak Convergence of Mixed Functionals -- 5.7 Examples -- 5.8 Auxiliary Results 6 Asymptotic Behavior of Homogeneous Additive Functionals of the Solutions to Inhomogeneous Itô SDEs with Non-regular Dependence on a Parameter -- 6.1 Preliminaries -- 6.2 Weak Compactness and Weak Convergence of the Solutions of Itô SDEs -- 6.3 Asymptotic Behavior of Integral Functionals of the Lebesgue Integral Type -- 6.4 Weak Convergence of Martingale Type Functional and of Mixed Functional -- 6.5 Examples -- 6.6 Auxiliary Results -- A Selected Facts and Auxiliary Results -- A.1 Selected Definitions and Facts for Stochastic Processes and Stochastic Integration
• Publisher Details: Cham : Springer
• Publication Date: 2020
• Extent: 1 online resource
• Subjects: 519.2/2; Stochastic differential equations; Stochastic differential equations; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783030412913; 3030412911
• Related ISBNs: 3030412903; 9783030412906
• Notes: Note: Includes bibliographical references.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.