title: Diffusions, Markov Processes and Martingales (Cambridge Mathematical Library)
author: L. C. G. Rogers
description: 'I welcome the paperback edition version of this masterfully written text.' Paul Embrechts, JASA<br /><br />'The monograph as a whole is warmly recommended to post-PhD students of probability and will be welcomed as a good and reliable reference.' EMS<br /><br />'... will be read with pleasure and advantage by experts in the field and its applications, as well as by those probabilists and others who wish to learn the subject ... an exciting and enjoyable introduction to the rich ideas of the It calculus ... there is nothing dry about this book, for its authors have already breathed life into a vibrant subject.' Mathematics Today
zlib_text: (C) The Author(s) 2015
  
  Makoto KatoriBessel Processes, Schramm-Loewner Evolution, and the Dyson
  ModelSpringerBriefs in Mathematical Physics1110.1007/978-981-10-0275-5_1
  
  # 1. Bessel Processes
  
  Makoto Katori1
  
  (1)
  
  Department of Physics, Chuo University, Tokyo, Japan
  
  Makoto Katori
  
  Email: [katori@phys.chuo-u.ac.jp](mailto:katori@phys.chuo-u.ac.jp)
  
  Abstract
  
  Basic notions of probability theory and stochastic analysis are explained
  using the Brownian motion and its functionals. The concepts of probability
  space and filtration are introduced, and the strong Markov property and the
  martingale property of Brownian motion are explained. A diffusion process is
  defined as a stochastic process having a continuous path almost surely with
  the strong Markov property. Quadratic variations and stochastic integrals are
  defined and Ito's formula is given which enables us to derive stochastic
  differential equations (SDEs) for diffusion processes. A D-dimensional Bessel
  process is originally defined as