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- Title
Approximating the First Passage Time Density of Diffusion Processes with State-Dependent Jumps.
- Authors
D'Onofrio, Giuseppe; Lanteri, Alessandro
- 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.
- Subjects
JUMP processes; JACOBI operators; PROBABILITY density function; RANDOM variables; HAMILTON-Jacobi equations; DENSITY
- Publication
Fractal & Fractional, 2023, Vol 7, Issue 1, p30
- ISSN
2504-3110
- Publication type
Article
- DOI
10.3390/fractalfract7010030