Search

We give criteria for the finiteness or infiniteness of the passage-time moments for continuous non-negative stochastic processes in terms of sub/supermartingale inequalities for powers of these processes. We apply these results to one-dimensional diffusions and also reflected Brownian motion in a wedge. The discrete-time analogue of this problem was studied previously by Lamperti and more recently by Aspandiiarov, Iasnogorodski and Menshikov [2]. Our results are continuous analogues of those in [2], but our proofs are direct and do not rely on approximation by discrete-time processes.

The asymptotic behavior of the first-passage-time p.d.f. through a constant boundary is studied when the boundary approaches the endpoints of the diffusion interval. We show that for a class of diffusion processes possessing a steady-state distribution this p.d.f. is approximately exponential, the mean being the average first-passage time to the boundary. The proof is based on suitable recursive expressions for the moments of the first-passage time.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

Passage-time moments for continuous non-negative stochastic processes and applications

Exponential trends of first-passage-time densities for a class of diffusion processes with steady-state distribution

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

Passage-time moments for continuous non-negative stochastic processes and applications

Exponential trends of first-passage-time densities for a class of diffusion processes with steady-state distribution