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Indian Statistical Institute Ser.: Introduction to Stochastic Calculus by B. V. Rao and Rajeeva L. Karandikar (2018, Hardcover)
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Title: Introduction to Stochastic Calculus (Indian Statistical Institut Item Condition: New. Book Details. Edition: 1st ed. 2018 List Price: -. ).
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About this product
Product Identifiers
PublisherSpringer
ISBN-109811083177
ISBN-139789811083174
eBay Product ID (ePID)242595998
Product Key Features
Number of PagesXiii, 441 Pages
LanguageEnglish
Publication NameIntroduction to Stochastic Calculus
SubjectProbability & Statistics / Stochastic Processes, Probability & Statistics / General, Calculus
Publication Year2018
TypeTextbook
AuthorB. V. Rao, Rajeeva L. Karandikar
Subject AreaMathematics
SeriesIndian Statistical Institute Ser.
FormatHardcover
Dimensions
Item Weight238 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Reviews"The style is compact and clear. The presentation is well complemented by a large number of useful remarks and exercises. Graduate students attending university courses in modern probability theory and its applications can benefit a lot from working with this book. There are good reasons to expect that the book will be met positively by students, university teachers and young researchers." (Jordan M. Stoyanov, zbMATH 1434.60003, 2020)
Number of Volumes1 vol.
IllustratedYes
Table Of ContentDiscrete Parameter Martingales.- Continuous Time Processes.- The Ito Integral.- Stochastic Integration.- Semimartingales.- Pathwise Formula for the Stochastic Integral.- Continuous Semimartingales.- Predictable Increasing Processes.- The Davis Inequality.- Integral Representation of Martingales.- Dominating Process of a Semimartingale.- SDE driven by r.c.l.l. Semimartingales.- Girsanov Theorem.
SynopsisDefines quadratic variation of a square integrable martingale Demonstrates pathwise formulae for the stochastic integral Uses the technique of random time change to study the solution of a stochastic differential equation Studies the predictable increasing process to introduce predictable stopping times and prove the Doob Meyer decomposition theorem Is useful for a two-semester graduate level course on measure theory and probability, This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly addresses continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier-Pellaumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- and beginning graduate-level students in the engineering and mathematics disciplines, the book is also an excellent reference resource for applied mathematicians and statisticians looking for a review of the topic.
LC Classification NumberQA276-280
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