000			02339nam a22003377a 4500
003			IIITD
005			20250524020003.0
008			250421b |||||||| |||| 00| 0 eng d
020			_a9783030564018
040			_aIIITD
082			_a519.2 _bKLE-P
100			_aKlenke, Achim
245	0	0	_aProbability theory : _ba comprehensive course _cby Achim Klenke
250			_a3rd ed.
260			_aLondon : _bSpringer, _c©2020
300			_axiv, 716 p. : _bill. ; _c24 cm.
504			_aIncludes bibliographical references and index.
505			_t1. Basic Measure Theory
505			_t2. Independence
505			_t3. Generating Functions
505			_t4. The Integral
505			_t5. Moments and Laws of Large Numbers
505			_t6. Convergence Theorems
505			_t7. L p -Spaces and the Radon-Nikodym Theorem
505			_t8. Conditional Expectations
520			_aProbabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineering and computer science. They help us to understand magnetism, amorphous media, genetic diversity and the perils of random developments on the financial markets, and they guide us in constructing more efficient algorithms. This text is a comprehensive course in modern probability theory and its measure-theoretical foundations. Aimed primarily at graduate students and researchers, the book 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 processes and infinite divisibility; large deviation principles and statistical physics; Brownian motion; and 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 the world of probability theory. In addition, plenty of figures, computer simulations, biographic details of key mathematicians, and a wealth of examples support and enliven the presentation.
650		0	_aProbability
650		0	_a"Mixing (mathematics)"
650		0	_aProbabilidade.
942			_2ddc _cBK _02
999			_c190003 _d190003