Lévy Processes

Code: MA782 | L-T-P-C: 4-0-0-8

MA782 Lévy Processes L-T-P-C [4-0-0-8]

Poisson random measures and their use in discontinuous martingales and LÉY processes; Brownian motion: Hitting times, maximum process, local times and excursions; Structure of local times and excursions in terms of Poisson random measures; LÉY processes: Structure and general properties, role of Brownian motion and Poisson random measures in the structure of LÉY processes, subordinators, hitting time of subordinators.

Texts:

1. E. Cinlar, Probability and Stochastics, Graduate Texts in Mathematics 261, Springer, 2011.
2. J. Bertoin, Lé Processes, Cambridge tracts in mathematics, Cambridge University Press, 1996.
3. K. Sato, Lé Processes and Infinitely Divisible Distributions, Revised edition, Cambridge studies in advanced mathematics, Cambridge University Press, 2013.