2020/01/24 by Shuwen Lou, Lou, Shuwen
Mathematics · Computer Science · Economics, Econometrics and Finance · #Spectral Theory in Mathematical Physics #Advanced Mathematical Modeling in Engineering #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2001.09226
In this paper, we study a particular model of distorted Brownian motion (dBM) on state spaces with varying dimension. Roughly speaking, the state space of such a process consists of two components: a 3-dimensional component and a 1-dimensional component. These two parts are joined together at the origin. The restriction of dBM on the 3- or 1-dimensional component receives a strong "push" towards the origin. On each component, the "magnitude" of the "push" can be parametrized by a constant γ>0. In this article, using probabilistic method, we get the exact expressions for the transition density functions of dBM with varying dimension for any 0