Some properties of density functions on maxima of one-dimensional diffusion processes

In the talk, we shall deal with one-dimensional stochastic differential equations (SDEs), and consider discrete and continuous time maximum of the solution. We will show some important properties of their probability density... [ view full abstract ]

In the talk, we shall deal with one-dimensional stochastic differential equations (SDEs), and consider discrete and continuous time maximum of the solution. We will show some important properties of their probability density functions. In particular, we shall obtain expressions, upper bounds and a convergence of the probability density functions by means of integration by parts formulas. The Key to prove the integration by parts formulas is the Malliavin calculus. If time permits, we will consider some other properties of the density functions which have been obtained recently.