BEHAVIOR OF THE FIRST HITTING TIME FOR A STRONGLY INWARD DIFFUSION

Let y is an element of R and (X(t)(y);t greater than or equal to 0) be the solution of the one-dimensional SDE: X(t)(y) = y + B-t - 1/2 inte gral(0)(t) u(X(s)(y))ds, where the drift -u is strongly inward (cf. (H -1) and (H-2) given below). We study the asymptotic behaviour of E(exp alpha T-x(y)), for y --> infinity, y greater than or equal to x great er than or equal to 0 and T-x(y) = inf{t greater than or equal to 0;X( t)(y) = x}.