Heat Kernel Method and its Applications

• Part I Analysis.- 1 Background in Analysis.- 2 Introduction to Partial Differential Equations.- Part II Geometry.- 3 Introduction to Differential Geometry.- Part III Perturbations.- 4 Singular Perturbations.- 5 Heat Kernel Asymptotics.- 6 Advanced Topics.- Part IV Applications.-  7 Stochastic Processes.- 8 Applications in Mathematical Finance.- Summary.-  References.- Index.

“Every chapter in this book contains a lot of information. Suggested further reading and precise references can be found at the end of each one. … It is aimed towards non-specialists, allowing them to quickly enter into the heart of the matters described above. This volume will be very useful to those interested in asymptotic expansions of heat kernels and stochastic models from financial mathematics.” (Pablo Raúl Stinga, Mathematical Reviews, July, 2017)“The main theme of the monograph is the development of a short-time expansion for the heat kernel. … The monograph is well organized; each chapter starts with an abstract and ends with a section of notes, that can be effectively used to navigate through the contents. Thanks to an extensive presentation of background material, the book is well suited for undergraduate and graduate students, but can be of interest also for applied mathematicians and physicists.” (Paolo Musolino, zbMATH 1342.35001, 2016)