Limit Theorems on Large Deviations for Markov Stochastic Processes, A.D. Wentzell

Автор: Jacod Jean, Shiryaev Albert N.
Название: Limit Theorems for Stochastic Processes
ISBN: 3540439323 ISBN-13(EAN): 9783540439325
Издательство: Springer
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Описание: Initially the theory of convergence in law of stochastic processes was developed quite independently from the theory of martingales, semimartingales and stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exposition of convergence in law for stochastic processes, from the point of view of semimartingale theory, with emphasis on results that are useful for mathematical theory and mathematical statistics. This leads them to develop in detail some particularly useful parts of the general theory of stochastic processes, such as martingale problems, and absolute continuity or contiguity results. The book contains an introduction to the theory of martingales and semimartingales, random measures stochastic integrales, Skorokhod topology, etc., as well as a large number of results which have never appeared in book form, and some entirely new results. The second edition contains some additions to the text and references. Some parts are completely rewritten.

Название: Large deviations and asymptotic methods in finance
ISBN: 3319116045 ISBN-13(EAN): 9783319116044
Издательство: Springer
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Описание:

Hagan, Lesniewski, Woodward: Probability Distribution in the SABR Model of Stochastic Volatility.- Paulot: Asymptotic Implied Volatility at the Second Order with Application to the SABR Model.- Henry-Labordere: Unifying the BGM and SABR Models: A Short Ride in Hyperbolic Geometry.- Ben Arous, Laurence: Second Order Expansion for Implied Volatility in Two Factor Local-stochastic Volatility.- Osajima: General Asymptotics of Wiener Functionals and Application to Implied Volatilities.- Bayer, Laurence: Small-time asymptotics for the at-the-money implied volatility in a multi-dimensional local volatility model.- Keller-Ressel, Teichmann: A Remark on Gatheral's 'Most-likely Path Approximation' of Implied Volatility.- Gatheral, Wang: Implied volatility from local volatility: a path integral approach.- Gerhold, Friz: Don't Stay Local - Extrapolation Analytics for Dupire's Local Volatility.- Gulisashvili, Teichmann: Laplace Principle Expansions and Short Time Asymptotics for Affine Processes.- Lorig, Pascucci, Pagliarani: Asymptotics for d-dimensional Levy-type Processes.- Takahashi: An Asymptotic Expansion Approach in Finance.- Baudoin, Ouyang: On small time asymptotics for rough differential equations driven by fractional Brownian motions.- Lucic: On singularities in the Heston model.- Bayer, Friz, Laurence: On the probability density function of baskets.- Conforti, De Marco, Deuschel: On small-noise equations with degenerate limiting system arising from volatility models.- Pham: Long time asymptotic problems for optimal investment.- Spiliopoulos: Systemic Risk and Default Clustering for Large Financial Systems.- Jacod, Rosenbaum: Asymptotic Properties of a Volatility Estimator.

Автор: Peter K. Friz; Jim Gatheral; Archil Gulisashvili;
Название: Large Deviations and Asymptotic Methods in Finance
ISBN: 3319385127 ISBN-13(EAN): 9783319385129
Издательство: Springer
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Цена: 16769.00 р.
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Описание:

Hagan, Lesniewski, Woodward: Probability Distribution in the SABR Model of Stochastic Volatility.- Paulot: Asymptotic Implied Volatility at the Second Order with Application to the SABR Model.- Henry-Labordere: Unifying the BGM and SABR Models: A Short Ride in Hyperbolic Geometry.- Ben Arous, Laurence: Second Order Expansion for Implied Volatility in Two Factor Local-stochastic Volatility.- Osajima: General Asymptotics of Wiener Functionals and Application to Implied Volatilities.- Bayer, Laurence: Small-time asymptotics for the at-the-money implied volatility in a multi-dimensional local volatility model.- Keller-Ressel, Teichmann: A Remark on Gatheral's 'Most-likely Path Approximation' of Implied Volatility.- Gatheral, Wang: Implied volatility from local volatility: a path integral approach.- Gerhold, Friz: Don't Stay Local - Extrapolation Analytics for Dupire's Local Volatility.- Gulisashvili, Teichmann: Laplace Principle Expansions and Short Time Asymptotics for Affine Processes.- Lorig, Pascucci, Pagliarani: Asymptotics for d-dimensional Levy-type Processes.- Takahashi: An Asymptotic Expansion Approach in Finance.- Baudoin, Ouyang: On small time asymptotics for rough differential equations driven by fractional Brownian motions.- Lucic: On singularities in the Heston model.- Bayer, Friz, Laurence: On the probability density function of baskets.- Conforti, De Marco, Deuschel: On small-noise equations with degenerate limiting system arising from volatility models.- Pham: Long time asymptotic problems for optimal investment.- Spiliopoulos: Systemic Risk and Default Clustering for Large Financial Systems.- Jacod, Rosenbaum: Asymptotic Properties of a Volatility Estimator.

Автор: L. Saulis; V.A. Statulevicius
Название: Limit Theorems for Large Deviations
ISBN: 0792314751 ISBN-13(EAN): 9780792314752
Издательство: Springer
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Описание: "Et moi, ...- si j'avait su comment en revenir. One service mathematics has rendered the je n'y serais poin t aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. H ea viside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service. topology has rendered mathematical physics .. .':: 'One service logic has rendered com- puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d 'e1: re of this series.

Автор: Mandjes, Michel
Название: Large deviations for gaussian queues
ISBN: 0470015233 ISBN-13(EAN): 9780470015230
Издательство: Wiley
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Описание: Demonstrates how the Gaussian traffic model arises naturally, and how the analysis of the corresponding queuing model can be performed. This text provides an introduction to Gaussian queues, and surveys research into the modelling of communications networks. It is useful for postgraduate students in applied probability, and operations research.

Автор: Sourav Chatterjee
Название: Large Deviations for Random Graphs
ISBN: 3319658158 ISBN-13(EAN): 9783319658155
Издательство: Springer
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Цена: 9781.00 р.
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Описание: This book addresses the emerging body of literature on the study of rare events in random graphs and networks.

Название: Limit Theorems for Stochastic Processes
ISBN: 144711051X ISBN-13(EAN): 9781447110514
Издательство: Springer
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Цена: 12157.00 р.
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Описание: This volume is the first to present a state-of-the-art overview of this field, with many results published for the first time. It covers the general conditions as well as the basic applications of the theory, and it covers and demystifies the vast and technically demanding Russian literature in detail.

Автор: Dudley
Название: Uniform Central Limit Theorems
ISBN: 0521738415 ISBN-13(EAN): 9780521738415
Издательство: Cambridge Academ
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Описание: This second edition of a classic work has been considerably expanded and revised, now with complete proofs of all results, including several new theorems not included in the first edition, such as Talagrand`s generic chaining approach to boundedness of Gaussian processes and Gine and Zinn`s characterization of uniform Donsker classes.

Автор: L. Arnold; P. Kotelenez
Название: Stochastic Space—Time Models and Limit Theorems
ISBN: 902772038X ISBN-13(EAN): 9789027720382
Издательство: Springer
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Цена: 13275.00 р.
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Описание: Approach your problems from It isn't that they can't see the right end and begin with the solution. the answers. Then one day, It is that they can't see the perhaps you will find the problem. final question. G.K. Chesterton. The Scandal 'The Hermit Clad 1n Crane of Father Brown 'The Point of Feathers' in R. van Gulik's a Pin'. The Chinese Maze Murders. Growing specialisation and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches wich were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.