Stochastic Analysis

The author is currently Professor Emeritus at The University of Tokyo and visiting Professor at Meiji University. He previously held positions at The University of Tokyo and Research Institute for Mathematical Sciences, Kyoto University. He was an invited speaker at the ICM 1990.

“This book is an introductory course on stochastic analysis for advanced students with previous knowledge in probability theory and measure theory. … The presentation of the theory is detailed and rigorous, both in terms of results and proofs. … The book can be an excellent textbook for an introductory course on stochastic analysis, with a strong emphasis on the central notion of martingales.” (Josep Vives, Mathematical Reviews, April, 2022)

• Chapter ​1. Preparations from probability theory.- Chapter 2. Martingale with discrete parameter.- Chapter 3. Martingale with continuous parameter.- Chapter 4. Stochastic integral.- Chapter 5. Applications of stochastic integral.- Chapter 6. Stochastic differential equation.- Chapter 7. Application to finance.- Chapter 8. Appendices.- References.