Three-dimensional Brownian motion and the golden ratio rule

Let X=(X_t)_{t\ge0} be a transient diffusion process in (0,\infty) with the diffusion coefficient \sigma>0 and the scale function L such that X_t\rightarrow\infty as t\rightarrow \infty, let I_t denote its running minimum for t\ge0, and let \theta denote the time of its ultimate minimum I_{\infty}. Setting c(i,x)=1-2L(x)/L(i) we show that the... Show more