Let $ X (t) $ be a stationary Gaussian process, $ f (t) $ a continuous function, and $ T $ a
finite or infinite interval. This paper develops asymptotic estimates for $ P (X (t)\geqslant f (t) …

Let p (t) be the density of the first-exit time of a Brownian motion over the one-sided moving
boundary given by x= f (t). We derive the following formal expansion for p: p (t) ∼ φ (t …

Let B t be a Brownian motion, g(t)=at+c, f(t)=bt+c, t≥ 0, a< b, c> 0, T> 0, and τ be the first
hitting time of B t either in f (t) or in g (t). We study the hitting probabilities …

Let B be a standard Brownian motion and let b_γ be a piecewise linear continuous
boundary function. In this paper we obtain an exact asymptotic expansion of …

The paper deals with curvilinear boundary crossing probabilities for time-homogeneous
diffusion processes. First we establish a relationship between the asymptotic form of …

The problem of approximating boundary hitting times for diffusion processes, and in
particular Brownian motion, is considered. Using a combination of probabilistic and function …

Let B=(B_t)_t\g0 be standard Brownian motion started at 0 under P, let S_t=0\lr\ltB_r be the
maximum process associated with B, and let g:\bfR_+→\bfR be a (strictly) monotone …

Let p (t) be the density of the first-exit time of a Brownian motion over a one-sided moving
boundary, and let p 1 (t) be the density at t of the first-exit time over the tangent to the …

Using the Girsanov transformation we derive estimates for the accuracy of piecewise
approximations for one-sided and two-sided boundary crossing probabilities. We …

Let w (t), 0≦ t≦∞, be a Brownian motion process, ie, a zero-mean separable normal
process with Pr {w (0)= 0}= 1, E {w (t1) w (t2)}= min (t1, t2), and let a, b denote the …