Ito and Stratonovich integrals on compound renewal processes: the normal/Poisson case

Germano, Guido, Politi, Mauro, Scalas, Enrico and Schilling, René L (2010) Ito and Stratonovich integrals on compound renewal processes: the normal/Poisson case. Communications in Nonlinear Science and Numerical Simulation, 15 (6). pp. 1583-1588. ISSN 1007-5704

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Abstract

Continuous-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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Depositing User: Enrico Scalas
Date Deposited: 25 Sep 2014 12:51
Last Modified: 25 Sep 2014 12:51
URI: http://sro.sussex.ac.uk/id/eprint/50249
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