Random motions at finite speed in higher dimensions
The author investigated the transport process \(X(t),t\geq 0\) in the Euclidean space \(\mathbb{R}^m, m\geq 2\). Based on the analysis of integral transforms of its distributions, the author proved that the joint characteristic function of \(X(t)\) are connected with each other by a convolution-type recurrent relation, and its characteristic function (Fourier transform) satisfies a convolution-type Volterra Integral equation of second kind. In particular, he got the Laplace transform of the characteristic function. Under the standard Kac condition on the speed of the motion and on intensity of the switching Poisson process, he proved the transition density of the isotropic transport process converges to the transition density of the \(m\)-dimensional homogeneous Brownian motion with zero drift and diffusion coefficient depending on the dimension \(m\). Finally he showed that the non-symmertrical random motions can also be treated by similar mothed.
scientific article; zbMATH DE number 5314329
scientific article