Rajeeva L. Karandikar and B. V. Rao
Introduction to Stochastic Calculus by Rajeeva L. Karandikar and B. V. Rao is a mathematically rigorous textbook that provides a clear and systematic introduction to the theory of stochastic calculus. The book begins with the foundations of probability theory and builds up to advanced topics such as martingales, Brownian motion, and Itô integrals. Its presentation is concise and precise, emphasizing proofs and logical development rather than heuristic explanations. The authors carefully construct each concept, ensuring that readers understand not only how stochastic calculus works but also why it works. Topics such as stochastic differential equations, Itô’s formula, and applications to finance and stochastic processes are developed with mathematical depth and clarity. The text is designed primarily for graduate students and researchers in mathematics, statistics, and related fields who seek a strong theoretical grounding. Exercises are thoughtfully chosen to reinforce understanding and challenge readers to engage with the material critically. Both authors are renowned probabilists, and their expertise ensures that the exposition is both authoritative and accessible to serious students. The book is known for bridging the gap between introductory probability courses and advanced research-level texts in stochastic analysis. It is published by Springer, as part of its Texts and Readings in Mathematics series from the Hindustan Book Agency (HBA).