TY  - GEN
AB  - This article shows that the nonstandard approach to stochastic integration with respect to (C^2 functions of) Lévy processes is consistent with the classical theory of pathwise stochastic integration with respect to (C^2 functions of) jump-diffusions with finite-variation jump part.
It is proven that internal stochastic integrals with respect to hyperfinite Lévy processes possess right standard parts, and that these standard parts coincide with the classical pathwise stochastic integrals, provided the integrator's jump part is of finite variation. If the integrator's Lévy measure is bounded from below, one can obtain a similar result for stochastic integrals with respect to C^2 functions of Lévy processes.
As a by-product, this yields a short, direct nonstandard proof of the generalized Itô formula for stochastic differentials of smooth functions of Lévy processes.
DA  - 2008
KW  - Itô formula
KW  - Nonstandard analysis
KW  - Lévy processes
KW  - Stochastic integration
LA  - eng
PY  - 2008
SN  - 0931-6558
TI  - Linear hyperfinite Lévy integrals
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:361-14220
Y2  - 2024-11-22T09:20:42
ER  -