Simulation of stochastic integrals with respect to Levy processes of type G
Wiktorsson, Magnus (2002). Simulation of stochastic integrals with respect to Levy processes of type G. Stochastic Processes and their Applications, 101, (1), 113 - 125
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Published
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English
Authors:
Wiktorsson, Magnus
Department:
Mathematical Statistics
Abstract:
We study the simulation of stochastic processes defined as stochastic integrals with respect to type G Levy processes for the case where it is not possible to simulate the type G process exactly. The type G Levy process as well as the stochastic integral can on compact intervals be represented as an infinite series. In a practical simulation we must truncate this representation. We examine the approximation of the remaining terms with a simpler process to get an approximation of the stochastic integral. We also show that a stochastic time change representation can be used to obtain an approximation of stochastic integrals with respect to type G Levy processes provided that the integrator and the integrand are independent.
Keywords:
stochastic time change ;
type G distribution ;
variance mixture ;
Levy ;
process ;
subordination ;
stochastic integral ;
shot noise representation
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