000			02223 a2200241 4500
003			OSt
005			20250113145722.0
008			250109b xxu||||| |||| 00| 0 eng d
020			_a9783030564018
040			_cIIT Kanpur
041			_aeng
082			_a519.2 _bK677p3
100			_aKlenke, Achim
245			_aProbability theory [3rd. ed.] _ba comprehensive course _cAchim Klenke
250			_a3rd ed.
260			_bSpringer _c2020 _aSwitzerland
300			_axiv, 716p
440			_aUniversitext
490			_a / edited by Sheldon Axlex
520			_a This popular textbook, now in a revised and expanded third edition, presents a comprehensive course in modern probability theory. Probability plays an increasingly important role not only in mathematics, but also in physics, biology, finance and computer science, helping to understand phenomena such as magnetism, genetic diversity and market volatility, and also to construct efficient algorithms. Starting with the very basics, this textbook covers a wide variety of topics in probability, including many not usually found in introductory books, such as: limit theorems for sums of random variables martingales percolation Markov chains and electrical networks construction of stochastic processes Poisson point process and infinite divisibility large deviation principles and statistical physics Brownian motion stochastic integrals and stochastic differential equations. The presentation is self-contained and mathematically rigorous, with the material on probability theory interspersed with chapters on measure theory to better illustrate the power of abstract concepts. This third edition has been carefully extended and includes new features, such as concise summaries at the end of each section and additional questions to encourage self-reflection, as well as updates to the figures and computer simulations. With a wealth of examples and more than 290 exercises, as well as biographical details of key mathematicians, it will be of use to students and researchers in mathematics, statistics, physics, computer science, economics and biology.
650			_aProbabilities
942			_cBK
999			_c567324 _d567324