This is a textbook for advanced undergraduate students and beginning graduate students in applied mathematics. It presents the basic mathematical foundations of

In 5 independent sections, this book accounts recent main developments of stochastic analysis: Gross-Stroock Sobolev space over a Gaussian probability space; qu

Stochastic analysis involves the study of a process involving a randomly determined sequence of observations, each of which represents a sample of one element o

This book is intended for university seniors and graduate students majoring in probability theory or mathematical finance. In the first chapter, results in prob

This book focuses on counting processes and continuous-time Markov chains motivated by examples and applications drawn from chemical networks in systems biology