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Fluctuations of Lévy Processes with Applications Introductory Lectures /

Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal...

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Bibliografiska uppgifter
Huvudupphovsman: Kyprianou, Andreas E. (Författare, medförfattare, http://id.loc.gov/vocabulary/relators/aut)
Institutionell upphovsman: SpringerLink (Online service)
Materialtyp: Elektronisk E-bok
Språk:English
Publicerad: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2014.
Upplaga:2nd ed. 2014.
Serie:Universitext,
Ämnen:
Probabilities.
Economics, Mathematical .
Probability Theory and Stochastic Processes.
Quantitative Finance.
Länkar:https://doi.org/10.1007/978-3-642-37632-0
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Innehållsförteckning:
  • Lévy Processes and Applications
  • The Lévy–Itô Decomposition and Path Structure
  • More Distributional and Path-Related Properties
  • General Storage Models and Paths of Bounded Variation
  • Subordinators at First Passage and Renewal Measures
  • The Wiener–Hopf Factorisation
  • Lévy Processes at First Passage
  • Exit Problems for Spectrally Negative Processes
  • More on Scale Functions
  • Ruin Problems and Gerber-Shiu Theory
  • Applications to Optimal Stopping Problems
  • Continuous-State Branching Processes
  • Positive Self-similar Markov Processes
  • Epilogue
  • Hints for Exercises
  • References
  • Index.

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