Format:
Online-Ressource (XIII, 434 p. 14 illus, digital)
Edition:
2nd ed. 2012
ISBN:
9780817683467
Series Statement:
Modeling and Simulation in Science, Engineering and Technology
Content:
Part I. The Theory of Stochastic Processes -- Fundamentals of Probability -- Stochastic Processes -- The Itô Integral -- Stochastic Differential Equations -- Part II. The Applications of Stochastic Processes -- Applications to Finance and Insurance -- Applications to Biology and Medicine -- Part III. Appendices -- Measure and Integration -- Convergence of Probability Measures on Metric Spaces -- Elliptic and Parabolic Operators -- D Semigroups and Linear Operators.- E Stability of Ordinary Differential Equations -- References.
Content:
From reviews of First Edition: The book is ... an account of fundamental concepts as they appear in relevant modern applications and literature. ... The book addresses three main groups: first, mathematicians working in a different field; second, other scientists and professionals from a business or academic background; third, graduate or advanced undergraduate students of a quantitative subject related to stochastic theory and/or applications. —Zentralblatt MATH This is an introductory text on continuous time stochastic processes and their applications to finance and biology. ... The book will be useful for applied mathematicians who are not probabilists to get a quick flavour of the techniques of stochastic calculus, and for professional probabilists to get a quick flavour of the applications. —Mathematical Reviews Revised and enhanced, this concisely written second edition of An Introduction to Continuous-Time Stochastic Processes is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Key topics include: * Markov processes * Stochastic differential equations * Arbitrage-free markets and financial derivatives * Insurance risk * Population dynamics * Agent-based models New to the Second Edition: * Improved presentation of original concepts * Expanded background on probability theory * Substantial material applicable to finance and biology, including stable laws, Lévy processes, and Itô-Lévy calculus * Supplemental appendix to provide basic facts on semigroups of linear operators An Introduction to Continuous-Time Stochastic Processes, Second Edition will be of interest to a broad audience of students, pure and applied mathematicians, and researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering. Suitable as a textbook for graduate or undergraduate courses, as well as European Masters courses (according to the two-year-long second cycle of the “Bologna Scheme”), the work may also be used for self-study or as a reference. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided.
Note:
Description based upon print version of record
,
An Introductionto Continuous-Time Stochastic Processes; Preface to the Second Edition; Preface to the First Edition; Contents; Part I Theory of Stochastic Processes; 1 Fundamentals of Probability; 1.1 Probability and Conditional Probability; 1.2 Random Variables and Distributions; 1.2.1 Random Vectors; 1.3 Independence; 1.4 Expectations; 1.5 Gaussian Random Vectors; 1.6 Conditional Expectations; 1.7 Conditional and Joint Distributions; 1.8 Convergence of Random Variables; Laws of Large Numbers for Independent Random Variables; 1.9 Infinitely Divisible Distributions; 1.9.1 Examples
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1.10 Stable Laws1.10.1 Martingales; 1.11 Exercises and Additions; 2 Stochastic Processes; 2.1 Definition; 2.2 Stopping Times; 2.3 Canonical Form of a Process; 2.4 Gaussian Processes; 2.5 Processes with Independent Increments; 2.6 Martingales; 2.7 Markov Processes; 2.8 Brownian Motion and the Wiener Process; 2.9 Counting, and Poisson Processes; 2.10 Marked Point Processes; 2.10.1 Random Measures; 2.10.2 Stochastic Intensities; 2.11 Lévy Processes; 2.12 Exercises and Additions; 3 The Itô Integral; 3.1 Definition and Properties; 3.2 Stochastic Integrals as Martingales
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3.3 Itô Integrals of Multidimensional Wiener Processes3.4 The Stochastic Differential; 3.5 Itô's Formula; 3.6 Martingale Representation Theorem; 3.7 Multidimensional Stochastic Differentials; 3.8 The Itô Integral with Respect to Lévy Processes; 3.9 The Itô-Lévy Stochastic Differential and the Generalized Itô Formula; 3.10 Exercises and Additions; 4 Stochastic Differential Equations; 4.1 Existence and Uniqueness of Solutions; 4.2 Markov Property of Solutions; 4.3 Girsanov Theorem; 4.4 Kolmogorov Equations; 4.5 Multidimensional Stochastic Differential Equations
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6.2 Population Dynamics: Continuous Approximationof Jump Models6.3 Population Dynamics: Individual-Based Models; 6.3.1 A Mathematical Detour; 6.3.2 A ``Moderate'' Repulsion Model; 6.3.3 Ant Colonies; 6.3.4 Price Herding; 6.4 Neurosciences; 6.5 Exercises and Additions; A Measure and Integration; A.1 Rings and -Algebras; A.2 Measurable Functions and Measure; A.3 Lebesgue Integration; A.4 Lebesgue-Stieltjes Measure and Distributions; A.5 Radon Measures; A.6 Stochastic Stieltjes Integration; B Convergence of Probability Measures on Metric Spaces; B.1 Metric Spaces; B.2 Prohorov's Theorem
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B.3 Donsker's Theorem
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4.6 Stability of Stochastic Differential Equations4.7 Itô-Lévy Stochastic Differential Equations; 4.7.1 Markov Property of Solutions of Itô-Lévy Stochastic Differential Equations; 4.8 Exercises and Additions; Part II Applications of Stochastic Processes; 5 Applications to Finance and Insurance; 5.1 Arbitrage-Free Markets; 5.2 The Standard Black-Scholes Model; 5.3 Models of Interest Rates; 5.4 Extensions and Alternatives to Black-Scholes; 5.5 Insurance Risk; 5.6 Exercises and Additions; 6 Applications to Biology and Medicine; 6.1 Population Dynamics: Discrete-in-Space-Continuous-in-TimeModels
Additional Edition:
ISBN 9780817683450
Additional Edition:
Buchausg. u.d.T. Capasso, Vincenzo, 1945 - An introduction to continuous-time stochastic processes New York, NY : Birkhäuser, 2012 ISBN 0817683453
Additional Edition:
ISBN 9780817683450
Language:
English
Subjects:
Mathematics
Keywords:
Stochastischer Prozess
;
Lehrbuch
DOI:
10.1007/978-0-8176-8346-7
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(lizenzpflichtig)
Author information:
Capasso, Vincenzo 1945-
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