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Document type:
Zeitschriftenaufsatz 
Author(s):
Klüppelberg, C., and Matsui, M. 
Title:
Generalized fractional Lévy processes with fractional Brownian motion limit and applications to stochastic volatility models 
Abstract:
Fractional Lévy processes generalize fractional Brownian motion in a natural way. We go a step further and extend the usual fractional Riemann-Liouville kernels to the more general class of regularly varying functions with the corresponding fractional integration parameter. The resulting stochastic processes are called generalized fractional Lévy processes (GFLP) which are shown to exhibit both short and long memory increments possibly with jumps. Moreover, for monotone kernels we define stoch...    »
 
Keywords:
Shot noise process, fractional Brownian motion, fractional Lévy process, generalized fractional Lévy process, fractional Ornstein-Uhlenbeck process, functional central limit theorem, regular variation, stochastic volatility model. 
Journal title:
Advances in Applied Probability 
Year:
2015 
Journal volume:
47 
Quarter:
4. Quartal 
Journal issue:
Pages contribution:
1108-1131 
Reviewed:
ja 
Language:
en 
Status:
Verlagsversion / published 
TUM Institution:
Lehrstuhl für Mathematische Statistik 
Format:
Text