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 jumpdiffusion process X(t), starting from x < S, we study the probability distribution of the integral AS(x) = ∫~( τS(x))_0 X(t) dt determined by X(t) till its first-crossing time τS(x) over S.