000			02427nam a2200265 4500
001			GB474
003			IN-BhIIT
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008			220104b ||||| |||| 00| 0 eng d
020			_a9781470419141
040			_aIN-BhIIT
041			_aeng
082			_a519.2 _bVAR/P
100			_aVaradhan S. R. S _eAuthor _917113
245			_aProbability Theory _cS. R. S. Varadhan and Louis Nirenberg
260			_aNew York : _bUniversities Press _c2001.
300			_a176 _c180 x 240 mm
490			_aAmerican Mathematical Society
504			_aIncludes Bibliographical references and Index.
520			_ahis volume presents topics in probability theory covered during a first-year graduate course given at the Courant Institute of Mathematical Sciences. The necessary background material in measure theory is developed, including the standard topics, such as extension theorem, construction of measures, integration, product spaces, Radon-Nikodym theorem, and conditional expectation. In the first part of the book, characteristic functions are introduced, followed by the study of weak convergence of probability distributions. Then both the weak and strong limit theorems for sums of independent random variables are proved, including the weak and strong laws of large numbers, central limit theorems, laws of the iterated logarithm, and the Kolmogorov three series theorem. The first part concludes with infinitely divisible distributions and limit theorems for sums of uniformly infinitesimal independent random variables. The second part of the book mainly deals with dependent random variables, particularly martingales and Markov chains. Topics include standard results regarding discrete parameter martingales and Doob's inequalities. The standard topics in Markov chains are treated, i.e., transience, and null and positive recurrence. A varied collection of examples is given to demonstrate the connection between martingales and Markov chains. Additional topics covered in the book include stationary Gaussian processes, ergodic theorems, dynamic programming, optimal stopping, and filtering. A large number of examples and exercises is included. The book is a suitable text for a first-year graduate course in probability.
650			_aProbabilities _917114
650			_aAmerican Mathematical Society _917115
700			_a Nirenberg , Louis _eJoint Author _917116
942			_cGB _01
999			_c12032 _d12032