Brownian Local Time of the Second Order at the Inverse Local Time Moment

According to the Ray–Knight description, the Brownian local time at the inverse local time moment with respect to the spatial variable is a diffusion process. This diffusion has a local time. Thus, we come to the definition of the local time of the initial Brownian local time. We will define such a process as the Brownian local time of the second order at the inverse local time moment. In this paper, we study the Laplace transform of the distribution of the Brownian local time of the second order.