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Cover: 9780521738651 | Levy Processes and Stochastic Calculus | David Applebaum | Taschenbuch
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Levy Processes and Stochastic Calculus
Taschenbuch von David Applebaum
Sprache: Englisch

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Beschreibung
Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.
Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.
Über den Autor
David Appelbaum has previously worked at a University as well as in publishing. His most recent books include notes on water: an aqueous phenomenology [Monkfish, 2018].
Zusammenfassung
A unique development of these two subjects contained in a single volume. New topics featured in this fully revised edition include regular variation and subexponential distributions, characterisation of Lévy processes with finite variation, multiple Wiener-Lévy integrals and chaos decomposition, and introductions to Malliavin calculus and stability theory for Lévy-driven SDEs.
Inhaltsverzeichnis
Preface to second edition; Preface to first edition; Overview; Notation; 1. Lévy processes; 2. Martingales, stopping times and random measures; 3. Markov processes, semigroups and generators; 4. Stochastic integration; 5. Exponential martingales; 6. Stochastic differential equations; References; Index of notation; Subject index.
Details
Erscheinungsjahr: 2014
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 492
ISBN-13: 9780521738651
ISBN-10: 0521738652
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Applebaum, David
Hersteller: Cambridge University Press
Maße: 229 x 152 x 29 mm
Von/Mit: David Applebaum
Erscheinungsdatum: 12.05.2014
Gewicht: 0,792 kg
preigu-id: 101645074
Über den Autor
David Appelbaum has previously worked at a University as well as in publishing. His most recent books include notes on water: an aqueous phenomenology [Monkfish, 2018].
Zusammenfassung
A unique development of these two subjects contained in a single volume. New topics featured in this fully revised edition include regular variation and subexponential distributions, characterisation of Lévy processes with finite variation, multiple Wiener-Lévy integrals and chaos decomposition, and introductions to Malliavin calculus and stability theory for Lévy-driven SDEs.
Inhaltsverzeichnis
Preface to second edition; Preface to first edition; Overview; Notation; 1. Lévy processes; 2. Martingales, stopping times and random measures; 3. Markov processes, semigroups and generators; 4. Stochastic integration; 5. Exponential martingales; 6. Stochastic differential equations; References; Index of notation; Subject index.
Details
Erscheinungsjahr: 2014
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 492
ISBN-13: 9780521738651
ISBN-10: 0521738652
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Applebaum, David
Hersteller: Cambridge University Press
Maße: 229 x 152 x 29 mm
Von/Mit: David Applebaum
Erscheinungsdatum: 12.05.2014
Gewicht: 0,792 kg
preigu-id: 101645074
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