This is a developing area of modern probability theory, which has applications in many areas. This volume is devoted to the systematic study of results on large deviations in situations where Cramér's condition on the finiteness of exponential moments may not be satisfied
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Inside This Book
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First Sentence:
In this section, we refine some results by Fortus (1957), Heyde (1968), A.V.Nagaev (1969), Feller (1971), Vol. II, Chapter 8, (8.14); and Tkachuk (1975, 1977), where the representation P{Sn > y} n c1 y-1 was established in various ranges of variation of the parameters n and y, under fulfilment of Condition (0.1) and other various constraints on the left-hand tail behavior of F. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
direct probabilistic method, conditioned limit theorems, second polar type, extreme value approximation, trimmed sums, stable limit law, subexponential distributions, maximal jump, power tails, negligible compare, tail approximation, refining terms, one big jump, auxiliary notation, exponential moments, individual summands, rightmost expression, exact asymptotics, large deviations, induction base, rightmost term, normal deviations, standard moments, tail behavior, subsequent combination Key Phrases - Capitalized Phrases (CAPs): (learn more)
Let Conditions, Applying Lemmas, Random Sums New!
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Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
In this section, we refine some results by Fortus (1957), Heyde (1968), A.V.Nagaev (1969), Feller (1971), Vol. II, Chapter 8, (8.14); and Tkachuk (1975, 1977), where the representation P{Sn > y} n c1 y-1 was established in various ranges of variation of the parameters n and y, under fulfilment of Condition (0.1) and other various constraints on the left-hand tail behavior of F. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
direct probabilistic method, conditioned limit theorems, second polar type, extreme value approximation, trimmed sums, stable limit law, subexponential distributions, maximal jump, power tails, negligible compare, tail approximation, refining terms, one big jump, auxiliary notation, exponential moments, individual summands, rightmost expression, exact asymptotics, large deviations, induction base, rightmost term, normal deviations, standard moments, tail behavior, subsequent combination Key Phrases - Capitalized Phrases (CAPs): (learn more)
Let Conditions, Applying Lemmas, Random Sums New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
Citations (learn more)
This book cites 16
books:
See all 16 books this book cites
3
books
cite this book:
- Regular Variation (Encyclopedia of Mathematics and its Applications) by N. H. Bingham in Back Matter (1), and Back Matter (2)
- Extreme Values (Monographs on Statistics and Probability) by R. L. Smith in Back Matter
- The Inverse Gaussian Distribution (Statistics: A Series of Textbooks and Monographs) by Raj Chhikara in Back Matter
- Random Perturbations of Dynamical Systems (Grundlehren der mathematischen Wissenschaften) by Mark I. Freidlin in Back Matter
- Extreme Values, Regular Variation, and Point Processes (Applied Probability) by Sidney I. Resnick in Back Matter
See all 16 books this book cites
- A Practical Guide to Heavy Tails: Statistical Techniques and Applications by Robert Adler on page 459
- Modelling Extremal Events: for Insurance and Finance (Stochastic Modelling and Applied Probability) by Paul Embrechts in Back Matter
- Advances on Theoretical and Methodological Aspects of Probability and Statistics by N. Balakrishnan on page 488
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