Question: If upon hitting the line La : w = a for the first time, the Brownian path is reflected in La, the resulting process is defined by
(ii) For the d-dimensional MBM w(t), define a reflected d-dimensional MBM in a sphere of radius a centered at the origin by
Obviously, |w∗(t)| ≤ a. Find the pdf of w∗(t), the partial differential equation, the initial conditions, and boundary conditions it satisfies on the sphere.