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MARC 21

Limit Theorems for Large Deviations
Tag	Description
020	$a9789401135306
082	$a519.2
099	$aOnline resource: Springer
100	$aSaulis, Leonas
245	$aLimit Theorems for Large Deviations$h[EBook]$cby L. Saulis, V. A. Statulevičius.
260	$aDordrecht$bSpringer Netherlands$c1991.
300	$aVIII, 232 pages$bonline resource.
336	$atext
338	$aonline resource
440	$aMathematics and its Applications, Soviet Series,$x0169-6378 ;$v73
505	$a1. The main notions -- 2. The main lemmas -- 2.1. General lemmas on the approximation of distribution of an arbitrary random variable by the normal distribution -- 2.2. Proof of lemmas 2.1—2.4 -- 3. Theorems on large deviations for the distributions of sums of independent random variables -- 3.1. Theorems on large deviations under Bernstein's condition -- 3.2. A theorem of large deviations in terms of Lyapunov's fractions -- 4. Theorems of large deviations for sums of dependent random variables -- 4.1. Estimates of the kth order centered moments of random processes with mixing -- 4.2. Estimates of mixed cumulants of random processes with mixing -- 4.3. Estimates of cumulants of sums of dependent random variables -- 4.4. Theorems and inequalities of large deviations for sums of dependent random variables -- 5. Theorems of large deviations for polynomial forms, multiple stochastic integrals and statistical estimates -- 5.1. Estimates of cumulants and theorems of large deviations for polynomial forms, polynomial Pitman estimates and U-statistics -- 5.2. Cumulants of multiple stochastic integrals and theorems of large deviations -- 5.3. Large deviations for estimates of the spectrum of a stationary sequence -- 6. Asymptotic expansions in the zones of large deviations -- 6.1. Asymptotic expansion for distribution density of an arbitrary random variable -- 6.2. Estimates for characteristic functions -- 6.3. Asymptotic expansion in the Cramer zone for distribution density of sums of independent random variables -- 6.4. Asymptotic expansions in integral theorems with large deviations -- 7. Probabilities of large deviations for random vectors -- 7.1. General lemmas on large deviations for a random vector with regular behaviour of cumulants -- 7.2. Theorems on large deviations for sums of random vectors and quadratic forms -- Appendices -- Appendix 1. Proof of inequalities for moments and Lyapunov's fractions -- Appendix 2. Proof of the lemma on the representation of cumulants -- Appendix 3. Leonov - Shiryaev’s formula -- References.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
700	$aStatulevičius, V. A.$eauthor.
710	$aSpringerLink (Online service)
830	$aMathematics and its Applications, Soviet Series,$v73
856	$uhttp://dx.doi.org/10.1007/978-94-011-3530-6