An Introduction to Continuous-Time Stochastic Processes : Theory, Models, and Applications to Finance, Biology, and Medicine / by Vincenzo Capasso, David Bakstein.

Format:

Book

Author/Creator:

Capasso, Vincenzo., Author.

Bakstein, David., Author.

Series:

Modeling and Simulation in Science, Engineering and Technology, 2164-3725

Language:

English

Subjects (All):

Probabilities.

Mathematical models.

Social sciences--Mathematics.

Social sciences.

Biomathematics.

Engineering mathematics.

Engineering--Data processing.

Engineering.

Probability Theory.

Mathematical Modeling and Industrial Mathematics.

Mathematics in Business, Economics and Finance.

Mathematical and Computational Biology.

Mathematical and Computational Engineering Applications.

Local Subjects:

Probability Theory.

Mathematical Modeling and Industrial Mathematics.

Mathematics in Business, Economics and Finance.

Mathematical and Computational Biology.

Mathematical and Computational Engineering Applications.

Physical Description:

1 online resource (XVI, 482 p. 14 illus.)

Edition:

3rd ed. 2015.

Place of Publication:

New York, NY : Springer New York : Imprint: Birkhäuser, 2015.

Language Note:

English

Summary:

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.

Contents:

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

ISBN:

1-4939-2757-4

OCLC:

1076255866