The explosion property of holomorphic diffusion processes on a bounded pseudoconvex domain in \(C^ n\) and its applications (Q1181056)

Let \(D\) be a bounded pseudoconvex domain in \(\mathbb{C}^ n\) and \(m\) be an everywhere dense positive Radon measure on \(D\). The sufficient conditions for a transient \(C^ \infty_ 0(D)\)-regular \(m\)-symmetric holomorphic diffusion process to explode in terms of the symmetrizing measure \(m\) is given. The boundary behaviour of plurisubharmonic functions along the sample path of the diffusion process is studied.