An introduction to continuous-time stochastic processes : theory, models, and applications to finance, biology, and medicine /

An introduction to continuous-time stochastic processes : theory, models, and applications to finance, biology, and medicine /

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Bibliographic Details
Author / Creator:Capasso, Vincenzo, 1945-
Edition:4th ed.
Imprint:Cham : Birkhäuser, 2021.
Description:1 online resource (574 p.).
Language:English
Series:Modeling and Simulation in Science, Engineering and Technology
Modeling and simulation in science, engineering & technology.
Subject:
Stochastic processes.
Stochastic processes -- Mathematical models.
Stochastic processes.
Stochastic processes -- Mathematical models.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/12613362
Hidden Bibliographic Details
Other authors / contributors:Bakstein, David, 1975-
ISBN:9783030696535
3030696537
9783030696528
3030696529
Notes:5.3 Stationary distributions.
Includes bibliographical references and index.
Online resource; title from PDF title page (SpringerLink, viewed June 28, 2021).
Summary:This textbook, now in its fourth edition, offers 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, it features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Unlike other books on stochastic methods that specialize in a specific field of applications, this volume examines the ways in which similar stochastic methods can be applied across di
Other form:Print version: Capasso, Vincenzo An Introduction to Continuous-Time Stochastic Processes Cham : Springer International Publishing AG,c2021 9783030696528
Standard no.:10.1007/978-3-030-69653-5
Table of Contents:
  • Intro
  • Foreword
  • Preface to the Fourth Edition
  • Preface to the Third Edition
  • 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
  • 1.4.1 Mixing inequalities
  • 1.4.2 Characteristic Functions
  • 1.5 Gaussian Random Vectors
  • 1.6 Conditional Expectations
  • 1.7 Conditional and Joint Distributions
  • 1.8 Convergence of Random Variables
  • 1.9 Infinitely Divisible Distributions
  • 1.9.1 Examples
  • 1.10 Stable Laws
  • 1.11 Martingales
  • 1.12 Exercises and Additions
  • 2 Stochastic Processes
  • 2.1 Definition
  • 2.2 Stopping Times
  • 2.3 Canonical Form of a Process
  • 2.4 L2 Processes
  • 2.4.1 Gaussian Processes
  • 2.4.2 Karhunen-Loève Expansion
  • 2.5 Markov Processes
  • 2.5.1 Markov Diffusion Processes
  • 2.6 Processes with Independent Increments
  • 2.7 Martingales
  • 2.7.1 The martingale property of Markov processes
  • 2.7.2 The martingale problem for Markov processes
  • 2.8 Brownian Motion and the Wiener Process
  • 2.9 Counting and Poisson Processes
  • 2.10 Random Measures
  • 2.10.1 Poisson random measures
  • 2.11 Marked Counting Processes
  • 2.11.1 Counting Processes
  • 2.11.2 Marked Counting Processes
  • 2.11.3 The Marked Poisson Process
  • 2.11.4 Time-space Poisson Random Measures
  • 2.12 White Noise
  • 2.12.1 Gaussian white noise
  • 2.12.2 Poissonian white noise
  • 2.13 Lévy Processes
  • 2.14 Exercises and Additions
  • 3 The Itô Integral
  • 3.1 Definition and Properties
  • 3.2 Stochastic Integrals as Martingales
  • 3.3 Itô Integrals of Multidimensional Wiener Processes
  • 3.4 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 Fractional Brownian Motion
  • 3.10.1 Integral with respect to a fBm
  • 3.11 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
  • 4.5.1 Multidimensional diffusion processes
  • 4.5.2 The time-homogeneous case
  • 4.6 Applications of Itô's Formula
  • 4.6.1 First Hitting Times
  • 4.6.2 Exit Probabilities
  • 4.7 Itô-Lévy Stochastic Differential Equations
  • 4.7.1 Markov Property of Solutions of Itô-Lévy Stochastic Differential Equations
  • 4.8 Exercises and Additions
  • 5 Stability, Stationarity, Ergodicity
  • 5.1 Time of explosion and regularity
  • 5.1.1 Application: A Stochastic Predator-Prey model
  • 5.1.2 Recurrence and transience
  • 5.2 Stability of Equilibria

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