Lévy matters V [Documento eletrónico] : functionals of Lévy processes / Lars Nørvang Andersen ... [et al.]
Language: eng.Country: Switzerland, Swiss Confederation.Publication: Cham : Springer International Publishing, 2015Description: XVI, 224 p. : il.ISBN: 978-3-319-23138-9.Series: Lévy Matters : A Subseries on Lévy Processes, 2149Subject - Topical Name: 6798Online Resources:Click here to access onlineItem type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | |
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QA273.SPR FCT 96301 Sharp martingale and semimartingale inequalities | QA273.SPR FCT 96335 Stochastic analysis, a series of lectures, Centre Interfacultaire Bernoulli, January–June 2012, Ecole Polytechnique Fédérale de Lausanne, Switzerland | QA273.SPR FCT 96338 Stochastic control theory, dynamic programming principle | QA273.SPR FCT 96411 Lévy matters V, functionals of Lévy processes | QA273.SPR FCT 96423 Lectures on the nearest neighbor method | QA273.SPR FCT 96432 Fractal geometry and stochastics V | QA273 SPR FCT 96444 Queues and Lévy fluctuation theory |
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This three-chapter volume concerns the distributions of certain functionals of Lévy processes. The first chapter, by Makoto Maejima, surveys representations of the main sub-classes of infinitesimal distributions in terms of mappings of certain Lévy processes via stochastic integration. The second chapter, by Lars Nørvang Andersen, Søren Asmussen, Peter W. Glynn and Mats Pihlsgård, concerns Lévy processes reflected at two barriers, where reflection is formulated à la Skorokhod. These processes can be used to model systems with a finite capacity, which is crucial in many real life situations, a most important quantity being the overflow or the loss occurring at the upper barrier. If a process is killed when crossing the boundary, a natural question concerns its lifetime. Deep formulas from fluctuation theory are the key to many classical results, which are reviewed in the third chapter by Frank Aurzada and Thomas Simon. The main part, however, discusses recent advances and developments in the setting where the process is given either by the partial sum of a random walk or the integral of a Lévy process. .
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