The lifetime of conditioned Brownian motion in an angular domain

Conditioned Brownian motions in bounded domains have been extensively studied.However, we know little about the conditioned processes in an unbounded domain for the difficulty of techniques and methods. Only a few peculiar cases are investigated. In this note, we shall be devoted to investigating the integrability of the lifetime of conditioned Brownian motions in the angular domain A_m^d={(x^1,…, x^d)∈R^d, x^i】0, 1≤i≤m≤d} (d≥2).