Mircea Grigoriu

Stochastic Calculus (eBook, PDF)

Applications in Science and Engineering

• Format: PDF

Produktbeschreibung

"Stochastic Calculus" focuses on analyzing and presenting solutions for a wide range of stochastic problems in applied mathematics, probability theory, physics, science, engineering, and finance. The author outlines essentials of probability theory, random processes, stochastic integration, and Monte Carlo simulation, then presents methods for solving problems defined by equations with deterministic and/or random coefficients and deterministic and/or stochastic inputs. This self-contained text may be used for graduate courses and as a reference for applied scientists interested in methods for solving stochastic problems.

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 775
• Erscheinungstermin: 11. Dezember 2013
• Englisch
• ISBN-13: 9780817682286
• Artikelnr.: 44203311

Autorenporträt

Grigoriu, M., Cornell University, Ithaca, USA

Inhaltsangabe

Introduction * Probability Theory * Stochastic Processes * Itô's Formula and Stochastic Differential Equations * Monte Carlo Simulation * Deterministic System and Input * Deterministic System and Stochastic Input * Stochastic System and Deterministic Input * Stochastic System and Stochastic Input * Bibliography * Index

Rezensionen

"When familiar at least with the basics of measure theoretic probability, one may use this book to get a feel for the type of problems one tackles with the given methods and the type of results one can expect and then proceed to more detailed expositions.... The book is an impressive achievement." -Mathematical Reviews

"The large number of examples...as well as the good survey on advanced mathematical techniques make the textbook very valuable for people working in mathematics with a view towards applications.... The applications range from climate dynamics over material sciences and mechanics to pattern formation, physics and finance. The presentation is very successful in providing a sound mathematical background without getting lost in too much technical detail. Most results are proved completely, for the others the main ideas and intuition are given and references for detailed expositions are given.... At the end of each chapter a list of instructive exercises is provided. The long list of references covers theoretical mathematical works as well as highly applied areas. Altogether this textbook has all the necessary prerequisites for boosting the interdisciplinary collaboration between applied scientists and probabilists." -Zentralblatt Math

"This is an impressive compendium, which, on its first 280 pages, provides a quite thorough review of probability theory, stochastic processes, Itô's formula and stochastic differential equations.... Although the focus is on the mathematical theory, many examples from sciences or engineering illustrate the concepts and methods. Each chapter ends with a number of problems. This book will be of substantial interest to the applied scientists seeking methods to solve stochastic problems." -Monatshefte für Mathematik