Fluctuation Theory for Lévy Processes
Doney, Ronald A.
Fluctuation Theory for Lévy Processes Ecole d'Eté de Probabilités de Saint-Flour XXXV - 2005 / [electronic resource] : by Ronald A. Doney ; edited by Jean Picard. - IX, 155 p. online resource. - École d'Été de Probabilités de Saint-Flour, 1897 0721-5363 ; . - École d'Été de Probabilités de Saint-Flour, 1897 .
to Lévy Processes -- Subordinators -- Local Times and Excursions -- Ladder Processes and the Wiener–Hopf Factorisation -- Further Wiener–Hopf Developments -- Creeping and Related Questions -- Spitzer's Condition -- Lévy Processes Conditioned to Stay Positive -- Spectrally Negative Lévy Processes -- Small-Time Behaviour.
Lévy processes, i.e. processes in continuous time with stationary and independent increments, are named after Paul Lévy, who made the connection with infinitely divisible distributions and described their structure. They form a flexible class of models, which have been applied to the study of storage processes, insurance risk, queues, turbulence, laser cooling, ... and of course finance, where the feature that they include examples having "heavy tails" is particularly important. Their sample path behaviour poses a variety of difficult and fascinating problems. Such problems, and also some related distributional problems, are addressed in detail in these notes that reflect the content of the course given by R. Doney in St. Flour in 2005.
9783540485117
10.1007/978-3-540-48511-7 doi
Distribution (Probability theory.
Probability Theory and Stochastic Processes.
QA273.A1-274.9 QA274-274.9
519.2
Fluctuation Theory for Lévy Processes Ecole d'Eté de Probabilités de Saint-Flour XXXV - 2005 / [electronic resource] : by Ronald A. Doney ; edited by Jean Picard. - IX, 155 p. online resource. - École d'Été de Probabilités de Saint-Flour, 1897 0721-5363 ; . - École d'Été de Probabilités de Saint-Flour, 1897 .
to Lévy Processes -- Subordinators -- Local Times and Excursions -- Ladder Processes and the Wiener–Hopf Factorisation -- Further Wiener–Hopf Developments -- Creeping and Related Questions -- Spitzer's Condition -- Lévy Processes Conditioned to Stay Positive -- Spectrally Negative Lévy Processes -- Small-Time Behaviour.
Lévy processes, i.e. processes in continuous time with stationary and independent increments, are named after Paul Lévy, who made the connection with infinitely divisible distributions and described their structure. They form a flexible class of models, which have been applied to the study of storage processes, insurance risk, queues, turbulence, laser cooling, ... and of course finance, where the feature that they include examples having "heavy tails" is particularly important. Their sample path behaviour poses a variety of difficult and fascinating problems. Such problems, and also some related distributional problems, are addressed in detail in these notes that reflect the content of the course given by R. Doney in St. Flour in 2005.
9783540485117
10.1007/978-3-540-48511-7 doi
Distribution (Probability theory.
Probability Theory and Stochastic Processes.
QA273.A1-274.9 QA274-274.9
519.2