The book "Multidimensional Diffusion Processes" by Daniel W. Stroock and S.R. Srinivasa Varadhan, originally published in 1997, is a comprehensive study in the field of mathematics, specifically focusing on multidimensional diffusion processes. The authors provide a detailed exploration of the theory and applications of these processes, covering topics such as extension theorems, martingales, compactness, Markov processes, Wiener measure, parabolic partial differential equations, stochastic calculus, stochastic differential equations, uniqueness, estimates on transition probability functions, explosion, limit theorems, and the non-unique case. The book is structured into several chapters, each delving into specific aspects of the subject, and includes exercises to reinforce understanding. The content is supported by a glossary of frequently used notation and a bibliography for further reference.The book "Multidimensional Diffusion Processes" by Daniel W. Stroock and S.R. Srinivasa Varadhan, originally published in 1997, is a comprehensive study in the field of mathematics, specifically focusing on multidimensional diffusion processes. The authors provide a detailed exploration of the theory and applications of these processes, covering topics such as extension theorems, martingales, compactness, Markov processes, Wiener measure, parabolic partial differential equations, stochastic calculus, stochastic differential equations, uniqueness, estimates on transition probability functions, explosion, limit theorems, and the non-unique case. The book is structured into several chapters, each delving into specific aspects of the subject, and includes exercises to reinforce understanding. The content is supported by a glossary of frequently used notation and a bibliography for further reference.