Some Remarks on the First-Crossing Area of a Diffusion Process with Jumps over a Constant Barrier

摘要

For a given barrier S ＞ 0 and a one-dimensional jump-diffusion process X(t), starting from x ＜ S, we study the probability distribution of the integral A_s(x) = ∫~(τ_s(x)) X(t) dt determined by X(t) till its first-crossing time τ_s(x) over S.