000 04246nam a22005415i 4500
001 978-1-4471-5361-0
003 DE-He213
005 20140220082455.0
007 cr nn 008mamaa
008 130829s2014 xxk| s |||| 0|eng d
020 _a9781447153610
_9978-1-4471-5361-0
024 7 _a10.1007/978-1-4471-5361-0
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aKlenke, Achim.
_eauthor.
245 1 0 _aProbability Theory
_h[electronic resource] :
_bA Comprehensive Course /
_cby Achim Klenke.
250 _a2nd ed. 2014.
264 1 _aLondon :
_bSpringer London :
_bImprint: Springer,
_c2014.
300 _aXII, 638 p. 46 illus., 20 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUniversitext,
_x0172-5939
505 0 _aBasic Measure Theory -- Independence -- Generating Functions -- The Integral -- Moments and Laws of Large Numbers -- Convergence Theorems -- Lp-Spaces and the Radon–Nikodym Theorem -- Conditional Expectations -- Martingales -- Optional Sampling Theorems -- Martingale Convergence Theorems and Their Applications -- Backwards Martingales and Exchangeability -- Convergence of Measures -- Probability Measures on Product Spaces -- Characteristic Functions and the Central Limit Theorem -- Infinitely Divisible Distributions -- Markov Chains -- Convergence of Markov Chains -- Markov Chains and Electrical Networks -- Ergodic Theory -- Brownian Motion -- Law of the Iterated Logarithm -- Large Deviations -- The Poisson Point Process -- The Itˆo Integral -- Stochastic Differential Equations.
520 _aThis second edition of the popular textbook contains a comprehensive course in modern probability theory. Overall, probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineering and computer science. They help us in understanding magnetism, amorphous media, genetic diversity and the perils of random developments at financial markets, and they guide us in constructing more efficient algorithms.   To address these concepts, the title covers a wide variety of topics, many of which are not usually found in introductory textbooks, 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 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.
650 0 _aMathematics.
650 0 _aDifferentiable dynamical systems.
650 0 _aFunctional analysis.
650 0 _aDistribution (Probability theory).
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aMeasure and Integration.
650 2 4 _aDynamical Systems and Ergodic Theory.
650 2 4 _aFunctional Analysis.
650 2 4 _aStatistical Physics, Dynamical Systems and Complexity.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781447153603
830 0 _aUniversitext,
_x0172-5939
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4471-5361-0
912 _aZDB-2-SMA
999 _c91869
_d91869