By D. Bakry, R. D. Gill, S. A. Molchanov
ISBN-10: 0387582088
ISBN-13: 9780387582085
This booklet includes work-outs of the notes of 3 15-hour classes of lectures which represent surveys at the involved issues given on the St. Flour chance summer time tuition in July 1992. the 1st path, via D. Bakry, is worried with hypercontractivity houses and their use in semi-group concept, particularly Sobolev and Log Sobolev inequa- lities, with estimations at the density of the semi-groups. the second, via R.D. Gill, is set data on survi- val research; it comprises product-integral concept, Kaplan- Meier estimators, and a glance at cryptography and iteration of randomness. The 3rd one, by means of S.A. Molchanov, covers 3 features of random media: homogenization thought, loca- lization homes and intermittency. every one of those chap- ters offers an creation to and survey of its topic.
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239-288). Dordrecht: Kluwer. Bruner, J. S. (1960). The process of education. Cambridge, MA: Harvard University Press. Cabrih, S. (1992). Filosofia de la probabilidad [Philosophy of probability]. Valencia, Spain: Tirant lo Blanc. Cardano, G. (1961). The book on games of chances. New York: Holt, Rinehart & Winston. (Original work Liber de Ludo Aleae; included in Opera Omnia, Vol. 1, published in 1663). Chaitin, G. J. (1975). A theory of program size formally identical to information theory. Journal of the Associationfor Computing Machinery, 22,329-340.
Let us consider, for example, the probability of getting at least one tail when flipping a coin twice. Some famous mathematicians gave different solutions to this simple problem because they applied different models for the sample space in this experiment. Thus, D'Alembert in 1776 argued in the French Encyclopedia that this probability was 213, since he considered three different equiprobable cases: getting a tail in the first flip (in this case the game is over), getting a head in the first flip and a tail in the second, or getting two successive heads.
Valencia, Spain: Tirant lo Blanc. Cardano, G. (1961). The book on games of chances. New York: Holt, Rinehart & Winston. (Original work Liber de Ludo Aleae; included in Opera Omnia, Vol. 1, published in 1663). Chaitin, G. J. (1975). A theory of program size formally identical to information theory. Journal of the Associationfor Computing Machinery, 22,329-340. Courtebras, B. (2001). Sur quelques conceptions du hasard [Regarding some conceptions of chance]. In M. ), Autour de la moddisation en probabilitks (pp.
Lectures on Probability Theory by D. Bakry, R. D. Gill, S. A. Molchanov
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