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This second edition of a popular textbook offers a comprehensive course in modern probability theory, emphasizing its growing significance across various fields such as mathematics, physics, biology, financial engineering, and computer science. The text explores essential probabilistic concepts that aid in understanding phenomena like magnetism, genetic diversity, and market randomness, while also contributing to the development of efficient algorithms. It covers diverse topics often absent from introductory texts, including limit theorems for sums of random variables, martingales, percolation, Markov chains, stochastic processes, Poisson point processes, large deviation principles, Brownian motion, and stochastic integrals and differential equations. The rigorous theory is presented in a self-contained manner, interweaving measure theory with probabilistic chapters to highlight the abstract concepts' power. This edition features extensive updates, including over 50 new figures, computer simulations, and more accessible proofs. With a wealth of examples, over 270 exercises, and biographical details of key mathematicians, it serves as a valuable resource for students and researchers in mathematics, statistics, physics, computer science, economics, and biology.
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Probability theory, Achim Klenke
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- Année de publication
- 2014
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