{"title":"Achim Klenke","description":"","products":[{"product_id":"probability-theory-book-achim-klenke-9783030564018","title":"Probability Theory","description":"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.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":49740922159377,"sku":"NGR9783030564018","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51061577154833,"sku":"NIN9783030564018","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52424279195921,"sku":"NLS9783030564018","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3030564010.jpg?v=1750806040"},{"product_id":"probability-theory-book-achim-klenke-9781447153603","title":"Probability Theory","description":"This second edition of the popular textbook contains a comprehensive course in modern probability theory, covering a wide variety of topics which are not usually found in introductory textbooks, including:  • 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 integral and stochastic differential equations.    The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in probability theory. This second edition has been carefully extended and includes many new features. It contains updated figures (over 50), computer simulations and some difficult proofs have been made more accessible. A wealth of examples and more than 270 exercises as well as biographic details of key mathematicians support and enliven the presentation. It will be of use to students and researchers in mathematics and statistics in physics, computer science, economics and biology.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":49990306365713,"sku":"CIN144715360XG","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/144715360X.jpg?v=1751241859"},{"product_id":"wahrscheinlichkeitstheorie-book-achim-klenke-9783662620885","title":"Wahrscheinlichkeitstheorie","description":"Seit seinem Erscheinen hat sich das Buch umgehend als Standardwerk fur eine umfassende und moderne Einfuhrung in die Wahrscheinlichkeitstheorie und ihre matheoretischen Grundlagen etabliert. Themenschwerpunkte sind: Ma- und Integrationstheorie, Grenzwertsatze fur Summen von Zufallsvariablen (Gesetze der Groen Zahl, Zentraler Grenzwertsatz, Ergodensatze, Gesetz vom iterierten Logarithmus, Invarianzprinzipien, unbegrenzt teilbare Verteilungen), Martingale, Perkolation, Markovketten und elektrische Netzwerke, Konstruktion stochastischer Prozesse, Poisson'scher Punktprozess, Brown'sche Bewegung, stochastisches Integral und stochastische Differentialgleichungen. Bei der Bearbeitung der Neuauflage wurde viel Wert auf eine noch zuganglichere didaktische Aufbereitung des Textes gelegt, und es wurden viele neue Abbildungen sowie Texterganzungen hinzugefugt.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52687777923345,"sku":"NLS9783662620885","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783662620885.jpg?v=1762331368"}],"url":"https:\/\/www.worldofbooks.com\/en-ie\/collections\/author-books-by-achim-klenke.oembed","provider":"World of Books ","version":"1.0","type":"link"}