Probability Theory Edited by K.A. Borovkov

作者:阁楼君

The book starts with with the introduction of probability spaces, goes on to random variables, then to the laws of large numbers, convergence notions, and the CLTs. It also discusses renewal theory, factorization identities, Markov chains, information and entropy, martingales, continuous time stocastic processes, functional limit theorems, and Markov processes.

Probability Theory


Edited by K.A. Borovkov



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The first text on Probability Theory was Huygens’ treatise De Ratiociniis in Ludo Alea (“On Ratiocination in Dice Games”, 1657). A bit later in 1663 the book Liber de Ludo Aleae (“Book on Games of Chance”) by G. Cardano was published (in fact it was written earlier, in the mid 16th century). The subject of these treatises was the same as in the writings of Fermat and Pascal: dice and card games (problems within the framework of Sect. 1.2 of the present book). As if Huygens foresaw future events, he wrote that if the reader studied the subject closely, he would notice that one was not dealing just with a game here, but rather that the foundations of a very interesting and deep theory were being laid. Huygens’ treatise, which is also known as the first text introducing the concept of mathematical expectation, was later included by J. Bernoulli in his famous book Ars Conjectandi (“The Art of Conjecturing”; published posthumously in 1713). To this book is related the notion of the so-called Bernoulli scheme (see Sect. 1.3), for which Bernoulli gave a cumbersome (cf. our Sect. 5.1) but mathematically faultless proof of the first limit theorem of Probability Theory, the Law of Large Numbers.


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