Modeling and Simulation in Science, Engineering and Technology / An Introduction to Continuous-Time Stochastic Processes
Theory, Models, and Applications to Finance, Biology, and Medicine
(Sprache: Englisch)
This textbook, now in its third 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, the...
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Produktinformationen zu „Modeling and Simulation in Science, Engineering and Technology / An Introduction to Continuous-Time Stochastic Processes “
This textbook, now in its third 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, 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, and epidemics
Agent-based models
New to the Third Edition:
Infinitely divisible distributions
Random measures
Levy processes
Fractional Brownian motion
Ergodic theory
Karhunen-Loeve expansion
Additional applications
Additional exercises
Smoluchowski approximation of Langevin systems
An Introduction to Continuous-Time Stochastic Processes, Third 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.
From reviews of previous editions:
"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
Key topics include:
Markov processes
Stochastic differential equations
Arbitrage-free markets and financial derivatives
Insurance risk
Population dynamics, and epidemics
Agent-based models
New to the Third Edition:
Infinitely divisible distributions
Random measures
Levy processes
Fractional Brownian motion
Ergodic theory
Karhunen-Loeve expansion
Additional applications
Additional exercises
Smoluchowski approximation of Langevin systems
An Introduction to Continuous-Time Stochastic Processes, Third 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.
From reviews of previous editions:
"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
Klappentext zu „Modeling and Simulation in Science, Engineering and Technology / An Introduction to Continuous-Time Stochastic Processes “
This textbook, now in its third 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, 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, and epidemics Agent-based models New to the Third Edition: Infinitely divisible distributions Random measures Levy processes Fractional Brownian motion Ergodic theory Karhunen-Loeve expansion Additional applications Additional exercises Smoluchowski approximation of Langevin systems An Introduction to Continuous-Time Stochastic Processes, Third 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. From reviews of previous editions: "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
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students of a quantitative subject related to stochastic theory and/or applications." -Zentralblatt MATH
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Inhaltsverzeichnis zu „Modeling and Simulation in Science, Engineering and Technology / An Introduction to Continuous-Time Stochastic Processes “
Part I: Theory of Stochastic Processes.- Fundamentals of Probability.- Stochastic Processes.- The Itô Integral.- Stochastic Differential Equations.- Stability, Stationary, Ergodicity.- Part II: Applications of Stochastic Processes.- Applications to Finance and Insurance.- Applications to Biology and Medicine.- Measure and Integration.- Convergence of Probability Measures on Metric Spaces.- Appendices.
Autoren-Porträt von Vincenzo Capasso, David Bakstein
Vincenzo Capasso is a Professor of Probability and Mathematical Statistics at the University of Milan. His research interests include spatially structured stochastic processes, stochastic geometry, reaction-diffusion systems, and statistics of structured stochastic processes. David Bakstein is a professor at the University of Milan, in ADAMSS (Interdisciplinary Center for Advanced Applied Mathematical and Statistical Sciences).
Bibliographische Angaben
- Autoren: Vincenzo Capasso , David Bakstein
- 2015, 3. Aufl., 482 Seiten, 14 Schwarz-Weiss-Abbildungen, Masse: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer, Berlin
- ISBN-10: 1493927566
- ISBN-13: 9781493927562
- Erscheinungsdatum: 29.05.2015
Sprache:
Englisch
Pressezitat
"This is indeed a very well written book on stochastic processes and their numerous applications. ... The reader will definitely benefit from the exercises given at the end of each of the chapters. ... The book is strongly recommended to students following any graduate program in mathematics and mathematical modeling. University teachers can easily use this book as a possible reference book for special intermediate and advanced courses in stochastics and its applications." (Jordan M. Stoyanov, zbMATH 1333.60002, 2016)Kommentar zu "Modeling and Simulation in Science, Engineering and Technology / An Introduction to Continuous-Time Stochastic Processes"
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