Explorations in Monte Carlo Methods

Ronald W. Shonkwiler is professor emeritus at Georgia Institute of Technology School of Mathematics. He received his PhD in 1970. His areas of expertise include: stochastic optimization, computer simulation, Monte Carlo numerical methods, mathematical biology, and reproducing Kernel Hilbert spaces.Franklin Mendivil is a professor at Acadia University in Nova Scotia. He received his BSCE in Civil Engineering and his PhD in 1996 at Georgia Institute of Technology. In addition to the first edition of this text, Professor Mendivil co-authored "Fractal-Based Methods in Analysis" 2012.

“This book is a joy to read cover to cover. Firstly, it is comprehensive in its treatment of the topics covered; containing interesting combination of techniques and encyclopaedic knowledge (on probability and number generators) that is hard to find in just (at an understandable level) one place elsewhere. … The book is littered with excellent, exciting and accessible … .” (physicsbookreviewer.blogspot.com, January 29, 2025)

• 1. Introduction to Monte Carlo Methods.- 2. Some Probability Distributions and Their Uses.- 3. Markov Chain Monte Carlo.- 4. Random Walks.- 5. Optimization by Monte Carlo Methods.- 6. More on Markov Chain Monte Carlo.- A. Generating Uniform Random Numbers.- B. Perron Frobenius Theorem.- C. Kelly Allocation for Correlated Investments.- D. Donsker's Theorem.- E. Projects.- References.- List of Notation.- Code Index.