Abstract
We study the problem of the first passage time through a constant boundary for a jump diffusion process whose infinitesimal generator is a nonlocal Jacobi operator. Due to the lack of analytical results, we address the problem using a discretization scheme for simulating the trajectories of jump diffusion processes with state-dependent jumps in both frequency and amplitude. We obtain numerical approximations on their first passage time probability density functions and results for the qualitative behavior of other statistics of this random variable. Finally, we provide two examples of application of the method for different choices of the distribution involved in the mechanism of generation of the jumps.
Funder
Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni
Subject
Statistics and Probability,Statistical and Nonlinear Physics,Analysis
Cited by
2 articles.
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