Stochastic Processes with Applications

This graduate work on stochastic processes provides a self- contained and systematic treatment of major topics such as random walk, Brownian motion, martingales, Markov chains indiscrete and continuous, stochastic optimization and stochastic differential equations. Beginning at a very simple technical level, the book gradually builds intuition and familiarity with techniques. For greater flexibility in instruction, some technical details are relegated to the end of each chapter under the label "theoretical complements". In this way the main body of the work becomes accessible to a wide range of readers, while the "theoretical complements" sections make the book mathematically complete for the more advanced reader.