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Ito and Stratonovich integrals on compound renewal processes: the normal/Poisson case
journal contribution
posted on 2023-06-08, 18:25 authored by Guido Germano, Mauro Politi, Enrico Scalas, René L SchillingContinuous-time random walks, or compound renewal processes, are pure-jump stochastic processes with several applications in insurance, finance, economics and physics. Based on heuristic considerations, a definition is given for stochastic integrals driven by continuous-time random walks, which includes the Itô and Stratonovich cases. It is then shown how the definition can be used to compute these two stochastic integrals by means of Monte Carlo simulations. Our example is based on the normal compound Poisson process, which in the diffusive limit converges to the Wiener process.
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Publication status
- Published
Journal
Communications in Nonlinear Science and Numerical SimulationISSN
1007-5704Publisher
ElsevierExternal DOI
Issue
6Volume
15Page range
1583-1588Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2014-09-25Usage metrics
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