Probability Theory: An Advanced Course
Π΄Π΅ΠΊ. 2012β―Π³. Β· Springer Science & Business Media
ΠΠ»Π΅ΠΊΡΡΠΎΠ½Π½Π°Ρ ΠΊΠ½ΠΈΠ³Π°
138
ΠΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΡΡΡΠ°Π½ΠΈΡ
reportΠΡΠ΅Π½ΠΊΠΈ ΠΈ ΠΎΡΠ·ΡΠ²Ρ Π½Π΅ ΠΏΡΠΎΠ²Π΅ΡΠ΅Π½Ρ. ΠΠΎΠ΄ΡΠΎΠ±Π½Π΅Π΅β¦
ΠΠ± ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΠΎΠΉ ΠΊΠ½ΠΈΠ³Π΅
This book presents a selection of topics from probability theory. Essentially, the topics chosen are those that are likely to be the most useful to someone planning to pursue research in the modern theory of stochastic processes. The prospective reader is assumed to have good mathematical maturity. In particular, he should have prior exposure to basic probability theory at the level of, say, K.L. Chung's 'Elementary probability theory with stochastic processes' (Springer-Verlag, 1974) and real and functional analysis at the level of Royden's 'Real analysis' (Macmillan, 1968). The first chapter is a rapid overview of the basics. Each subsequent chapter deals with a separate topic in detail. There is clearly some selection involved and therefore many omissions, but that cannot be helped in a book of this size. The style is deliberately terse to enforce active learning. Thus several tidbits of deduction are left to the reader as labelled exercises in the main text of each chapter. In addition, there are supplementary exercises at the end. In the preface to his classic text on probability ('Probability', Addison Wesley, 1968), Leo Breiman speaks of the right and left hands of probability.
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Π§ΡΠΎΠ±Ρ ΠΎΡΠΊΡΡΡΡ ΠΊΠ½ΠΈΠ³Ρ Π½Π° ΡΠ°ΠΊΠΎΠΌ ΡΡΡΡΠΎΠΉΡΡΠ²Π΅ Π΄Π»Ρ ΡΡΠ΅Π½ΠΈΡ, ΠΊΠ°ΠΊ Kobo, ΡΠΊΠ°ΡΠ°ΠΉΡΠ΅ ΡΠ°ΠΉΠ» ΠΈ Π΄ΠΎΠ±Π°Π²ΡΡΠ΅ Π΅Π³ΠΎ Π½Π° ΡΡΡΡΠΎΠΉΡΡΠ²ΠΎ. ΠΠΎΠ΄ΡΠΎΠ±Π½ΡΠ΅ ΠΈΠ½ΡΡΡΡΠΊΡΠΈΠΈ ΠΌΠΎΠΆΠ½ΠΎ Π½Π°ΠΉΡΠΈ Π² Π‘ΠΏΡΠ°Π²ΠΎΡΠ½ΠΎΠΌ ΡΠ΅Π½ΡΡΠ΅.
