An Advanced Course in Probability and Stochastic Processes

ISBN-13: 9781032320465 / Twarda / 2023 / 384 str.

Australia) Botev Zdravko (University of New South Wales

Opis

An Advanced Course in Probability and Stochastic Processes provides a modern and rigorous treatment of probability theory and stochastic processes at an upper undergraduate and graduate level. Fundamental stochastic processes are explored in considerable depth

Spis treści

1. Measure Theory  2. Probability  3. Convergence  4. Conditioning  5. Martingales  6. Wiener and Brownian Motion Processes  7. Itô Calculus  Appendix A. Selected Solutions  Appendix B. Function Spaces  Appendix C. Existence of the Lebesgue Measure  Index

O autorze

Dirk P. Kroese, PhD, is a Professor of Mathematics and Statistics at The University of Queensland. He has published over 140 articles and seven books in a wide range of areas in applied probability, mathematical statistics, data science, machine learning, and Monte Carlo methods. He is a pioneer of the well-known Cross-Entropy method—an adaptive Monte Carlo technique, which is being used around the world to help solve difficult estimation and optimization problems in science, engineering, and finance.

Zdravko Botev, PhD, teaches Computational Statistics and Applied Probability at the University of New South Wales in Sydney, Australia. He is the recipient of the 2018 Christopher Heyde Medal of the Australian Academy of Science for distinguished research in the Mathematical Sciences and the 2019 Gavin Brown prize for his work on kernel density estimation, for which he is the author of one of the most widely used Matlab software scripts.