On the continuity of plurisubharmonic functions along conformal diffusions (Q1819817)

A process \(Z_ t=(Z^ 1_ t,...,Z^ n_ t)\) with values in \({\mathbb{C}}^ n\) is a conformal martingale if for each i,j, \(Z^ i_ t\) and \(Z^ i_ tZ^ j_ t\) are complex martingales. If M is a complex manifold of dimension n, a diffusion Z on M is conformal if it is locally a conformal martingale in each set of holomorphic local coordinates. The author shows that if u is a plurisubharmonic function on M and Z a conformal diffusion, then \(u(Z_ t)\) is almost surely continuous up to its lifetime.