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

作者：Germano Guido; Politi Mauro; Scalas Enrico^*; Schilling Rene L

来源：Communications in Nonlinear Science & Numerical Simulation, 2010, 15(6): 1583-1588.

DOI：10.1016/j.cnsns.2009.06.010

• Continuous-time random walk
• Stochastic integrals
• Stochastic jump process
• Stochastic theory
• Stochastic model
• Probabilistic model
• Probabilistic simulation
• Monte Carlo
• Econophysics

Continuous-time random walks, or compound renewal processes, are pure-jump stochastic processes with several applications in insurance, finance, economics and physics. Based oil heuristic considerations. a definition is given for stochastic integrals driven by continuous-time random walks, which includes the Ito and Stratonovich cases. It is their 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.