Jump SDEs and the Study of Their Densities

Professor Kohatsu-Higa is a professor at Ritsumeikan University and Professor Takeuchi is a professor at Tokyo Woman's Christian University.

• Review of some basic concepts of probability theory.- Simple Poisson process and its corresponding SDEs.- Compound Poisson process and its associated stochastic calculus.- Construction of Lévy  processes and their corresponding SDEs: The finite variation case.- Construction of Lévy  processes and their corresponding SDEs: The infinite variation case.- Multi-dimensional Lévy processes and their densities.- Flows associated with stochastic differential equations with jumps.- Overview.- Techniques to study the density.- Basic ideas for integration by parts formulas.- Sensitivity formulas.- Integration by parts: Norris method .- A non-linear example: The Boltzmann equation.- Further hints for the exercises

“The book is very friendly to the reader because the authors give all necessary instructions for the non-experienced reader that are also useful for any reader … . the book is devoted to very topical issues appearing in such fields as economy, finance, techniques and many others. Therefore, reading this book is both work and pleasure, and the book can be recommended to both undergraduate and graduate students, specialists in probability theory and its applications.” (Yuliya S. Mishura, zbMATH 1447.60001, 2020)“The book is very well written and presented, and nicely oriented to self-study with many exercises. I strongly recommend this excellent book to all graduate students and researchers interested in stochastic calculus of jump processes or in modeling using jump processes, in any subject.” (Josep Vives, Mathematical Reviews, October, 2020)“This book is written mainly for advanced undergraduate and graduate students and researchers that are interested in this field and it can bring the reader very soon to a research level. The list of references are complete and guide the researcher to more specific and advanced topics.” (Nikos Halidias, MAA Reviews, August 16, 2020)