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

详细信息    查看全文

• 作者：Guido Germano ; Mauro Politi ; Enrico Scalas ; René ; L. Schilling
• 关键词：Continuous-time random walk ; Stochastic integrals ; Stochastic jump process ; Stochastic theory ; Stochastic model ; Probabilistic model ; Probabilistic simulation ; Monte Carlo ; Econophysics
• 刊名：Communications in Nonlinear Science and Numerical Simulation
• 出版年：2010
• 出版时间：June 2010
• 年：2010
• 卷：15
• 期：6
• 页码：1583-1588
• 全文大小：269 K

文摘

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.