Space-time processes, parabolic functions and one-dimensional diffusions
Space-time processes, parabolic functions and one-dimensional diffusions
In this paper, we study the properties of the space-time process and of parabolic functions associated with a Markov process. Making use of these properties and the asymptotic behavior of the first passage probabilities near the boundary points, we prove certain theorems concerning when $u(X(t),t)$ is a martingale, where $X(t)$ …