By Jeffrey S. Rosenthal
Книга дает строгое изложение всех базовых концепций теории вероятностей на основе теории меры, в то же время не перегружая читателя дополнительными сведениями. В книге даются строгие доказательства закона больших чисел, центральной предельной теоремы, леммы Фату, формулируется лемма Ито. В тексте и математическом приложении содержатся все необходимые сведения, так что книга доступна для понимания любому выпускнику школы.This textbook is an advent to chance concept utilizing degree idea. it's designed for graduate scholars in numerous fields (mathematics, facts, economics, administration, finance, laptop technology, and engineering) who require a operating wisdom of chance conception that's mathematically special, yet with out over the top technicalities. The textual content presents whole proofs of all of the crucial introductory effects. however, the remedy is concentrated and available, with the degree idea and mathematical information awarded when it comes to intuitive probabilistic ideas, instead of as separate, enforcing topics. during this new version, many workouts and small extra themes were further and present ones extended. The textual content moves a suitable stability, carefully constructing likelihood concept whereas warding off pointless detail.
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Extra resources for A first look at rigorous probability theory
Yakowitz, S. and E. Lugosi. (1990). Random search in the presence of noise, with application to machine learning. SIAM J. Sci. Statist. Comput. 11, 702712. , J. Gani, and R. Hayes. (1990). Cellular automaton modeling of epidemics. Appl. Math. Comput. 40, 41-54. Rutherford, B. and S. Yakowitz. (1991). Error inference for nonparametric regression. Ann. Inst. Statist. Math. 43, 115-129. Yakowitz, S. and W. Lowe. (1991). Nonparametric bandit methods. Ann. Operat. Res. 28, 297-312. D. and S. Yakowitz.
Szidarovszky, F, S. Yakowitz, and R. Krzysztofowicz. (1975). A Bayes approach for simulating sediment yield. J. Hydrol. Sci. 3, 33-45. Fisher, L. and S. Yakowitz. (1976). Uniform convergence of the potential function algorithm. SIAM J. Control Optim. 14, 95-103. Yakowitz, S. (1976). Small sample hypothesis tests of Markov order with application to simulated and hydrologic chains. J. Amer. Statist. Assoc. 71, 132-136. Yakowitz, S. and P. Noren. (1976) On the identification of inhomogeneous parameters in dynamic linear partial differential equations.
Inform. Theory 39, 1031-1036. , B. Kedem, and S. Yakowitz. (1994). Asymptotic normality of sample autocovariances with an application in frequency estimation. Stoch. Proc. Appl. 52, 329-349. Pinelis, I. and S. Yakowitz. (1994). The time until the final zero-crossing of random sums with application to nonparametric bandit theory. Appl. Math. Comput. 63, 235-263. Kedem, B. and S. Yakowitz. (1994). Practical aspects of a fast algorithm for frequency detection. IEEE Trans. Commun. 42, 2760-2767. Yakowitz, S.