☆ 4.2 Article

Exact solution to a first-passage problem for an Ornstein-Uhlenbeck process with jumps and its integral

STATISTICS & PROBABILITY LETTERS (2024)

Related references

Note: Only part of the references are listed.

Article Mathematics, Interdisciplinary Applications

First-Passage Times and Optimal Control of Integrated Jump-Diffusion Processes

Mario Lefebvre

Summary: This paper considers a one-dimensional jump-diffusion process Y(t) and a process X(t) defined by dX(t) = p[X(t), Y(t)] dt, where p(·, ·) is a strictly positive or negative function. First-passage-time problems for the degenerate two-dimensional process (X(t), Y(t)) are discussed when the process leaves the continuation region at the latest at the moment of the first jump, and the optimal control problem is also treated. A particular problem, where p[X(t), Y(t)] = Y(t) - X(t) and Y(t) is a standard Brownian motion with jumps, is solved explicitly.

FRACTAL AND FRACTIONAL (2023)

Add to Collection

Article Mathematics, Applied