Overview
- Discusses quadratic variation of a square integrable martingale, pathwise formulae for the stochastic integral, Emery topology, and sigma-martingales
- Uses the technique of random time change to study the solution of a stochastic differential equation (SDE) driven by continuous semi-martingales
- Studies the predictable increasing process to introduce predictable stopping times and to prove the Doob–Meyer decomposition theorem
- Gives an extensive treatment of representation of martingales as stochastic integrals
- Is useful for a two-semester graduate-level course on measure-theoretic probability
Part of the book series: Indian Statistical Institute Series (INSIS)
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Table of contents (13 chapters)
Keywords
About this book
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)
Authors and Affiliations
About the authors
B.V. Rao is an adjunct professor at Chennai Mathematical Institute, Tamil Nadu, India. He received his MSc degree in Statistics from Osmania University, Hyderabad, India, in 1965 and the doctoral degree from the Indian Statistical Institute, Kolkata, India, in 1970. His research interests include descriptive set theory, analysis, probability theory and stochastic calculus. He was a professor and later a distinguished scientist at the Indian Statistical Institute, Kolkata. Generations of Indian probabilists have benefitted from his teaching, where he taught from 1973 till 2009.
Bibliographic Information
Book Title: Introduction to Stochastic Calculus
Authors: Rajeeva L. Karandikar, B. V. Rao
Series Title: Indian Statistical Institute Series
DOI: https://doi.org/10.1007/978-981-10-8318-1
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2018
Hardcover ISBN: 978-981-10-8317-4Published: 15 June 2018
Softcover ISBN: 978-981-13-4121-2Published: 10 January 2019
eBook ISBN: 978-981-10-8318-1Published: 01 June 2018
Series ISSN: 2523-3114
Series E-ISSN: 2523-3122
Edition Number: 1
Number of Pages: XIII, 441
Topics: Statistical Theory and Methods, Probability Theory and Stochastic Processes