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001437599 020__ $$a9783030696535$$q(electronic bk.)
001437599 020__ $$a3030696537$$q(electronic bk.)
001437599 020__ $$z9783030696528$$q(print)
001437599 020__ $$z3030696529
001437599 0247_ $$a10.1007/978-3-030-69653-5$$2doi
001437599 035__ $$aSP(OCoLC)1257665568
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001437599 049__ $$aISEA
001437599 050_4 $$aQA274
001437599 08204 $$a519.2/3$$223
001437599 1001_ $$aCapasso, Vincenzo,$$d1945-
001437599 24513 $$aAn introduction to continuous-time stochastic processes :$$btheory, models, and applications to finance, biology, and medicine /$$cVincenzo Capasso, David Bakstein.
001437599 250__ $$a4th ed.
001437599 260__ $$aCham :$$bBirkhäuser,$$c2021.
001437599 300__ $$a1 online resource (574 pages)
001437599 336__ $$atext$$btxt$$2rdacontent
001437599 337__ $$acomputer$$bc$$2rdamedia
001437599 338__ $$aonline resource$$bcr$$2rdacarrier
001437599 4901_ $$aModeling and Simulation in Science, Engineering and Technology
001437599 500__ $$a5.3 Stationary distributions.
001437599 504__ $$aIncludes bibliographical references and index.
001437599 5050_ $$aIntro -- Foreword -- Preface to the Fourth Edition -- Preface to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- Part I Theory of Stochastic Processes -- 1 Fundamentals of Probability -- 1.1 Probability and Conditional Probability -- 1.2 Random Variables and Distributions -- 1.2.1 Random Vectors -- 1.3 Independence -- 1.4 Expectations -- 1.4.1 Mixing inequalities -- 1.4.2 Characteristic Functions -- 1.5 Gaussian Random Vectors -- 1.6 Conditional Expectations -- 1.7 Conditional and Joint Distributions -- 1.8 Convergence of Random Variables
001437599 5058_ $$a1.9 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
001437599 5058_ $$a2.9 Counting and Poisson Processes -- 2.10 Random Measures -- 2.10.1 Poisson random measures -- 2.11 Marked Counting Processes -- 2.11.1 Counting Processes -- 2.11.2 Marked Counting Processes -- 2.11.3 The Marked Poisson Process -- 2.11.4 Time-space Poisson Random Measures -- 2.12 White Noise -- 2.12.1 Gaussian white noise -- 2.12.2 Poissonian white noise -- 2.13 Lévy Processes -- 2.14 Exercises and Additions -- 3 The Itô Integral -- 3.1 Definition and Properties -- 3.2 Stochastic Integrals as Martingales -- 3.3 Itô Integrals of Multidimensional Wiener Processes
001437599 5058_ $$a3.4 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
001437599 5058_ $$a4.5 Multidimensional Stochastic Differential Equations -- 4.5.1 Multidimensional diffusion processes -- 4.5.2 The time-homogeneous case -- 4.6 Applications of Itô's Formula -- 4.6.1 First Hitting Times -- 4.6.2 Exit Probabilities -- 4.7 Itô-Lévy Stochastic Differential Equations -- 4.7.1 Markov Property of Solutions of Itô-Lévy Stochastic Differential Equations -- 4.8 Exercises and Additions -- 5 Stability, Stationarity, Ergodicity -- 5.1 Time of explosion and regularity -- 5.1.1 Application: A Stochastic Predator-Prey model -- 5.1.2 Recurrence and transience -- 5.2 Stability of Equilibria
001437599 506__ $$aAccess limited to authorized users.
001437599 520__ $$aThis textbook, now in its fourth edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, it features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Unlike other books on stochastic methods that specialize in a specific field of applications, this volume examines the ways in which similar stochastic methods can be applied across di
001437599 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed June 28, 2021).
001437599 650_0 $$aStochastic processes.
001437599 650_0 $$aStochastic processes$$xMathematical models.
001437599 650_6 $$aProcessus stochastiques.
001437599 650_6 $$aProcessus stochastiques$$xModèles mathématiques.
001437599 655_0 $$aElectronic books.
001437599 7001_ $$aBakstein, David,$$d1975-
001437599 77608 $$iPrint version:$$aCapasso, Vincenzo.$$tAn Introduction to Continuous-Time Stochastic Processes.$$dCham : Springer International Publishing AG, ©2021$$z9783030696528
001437599 830_0 $$aModeling and simulation in science, engineering & technology.
001437599 852__ $$bebk
001437599 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-69653-5$$zOnline Access$$91397441.1
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001437599 980__ $$aBIB
001437599 980__ $$aEBOOK
001437599 982__ $$aEbook
001437599 983__ $$aOnline
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