LĘVY PROCESSES AND STOCHASTIC CALCULUS

Opis produktu

David Applebaum is a Professor in the Department of Probability and Statistics at the University of Sheffield.A fully revised and appended edition of this unique volume which develops together these two important subjects.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 Lęvy processes with finite variation multiple WienerLęvy integrals and chaos decomposition and introductions to Malliavin calculus and stability theory for Lęvydriven SDEs.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 Lęvy processes with finite variation multiple WienerLęvy integrals and chaos decomposition and introductions to Malliavin calculus and stability theory for Lęvydriven SDEs.Lęvy 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 Lęvy processes then leading on to develop the stochastic calculus for Lęvy 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 Lęvy processes to have finite moments: characterisation of Lęvy processes with finite variation: Kunitas estimates for moments of Lęvy type stochastic integrals: new proofs of Ito representation and martingale representation theorems for general Lęvy processes: multiple WienerLęvy integrals and chaos decomposition: an introduction to Malliavin calculus: an introduction to stability theory for Lęvydriven SDEs.Preface to second edition: Preface to first edition: Overview: Notation: 1. Lęvy 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.The book introduces all the tools that are needed for the stochastic approach to option pricing including Its formula Girsanovs theorem and the martingale representation theorem. LEnseignement MathęmatiqueThe monograph provides a good introduction to the subject the exposition is clear and systematic the key points and proofs are easy to follow: therefore it can be a valuable guide both as a textbook for graduate students and as a reference for researchers in the field of stochiastic calculus This book is written with great care and precision. Due to its lucid and comprehensive style of presentation it will make the theory of Lęvy processes accessible to a broad m

Data Publikacji: 2009-04-30
Wymiary: 228 mm 152 mm 25 mm 730 gr