We provide the explicit solutions of linear, left-invariant, (convection)-diffusion equations and the corresponding resolvent equations on the 2D-Euclidean motion group SE(2) = RoT. These diffusion equations are forward Kolmogorov equations for well-known stochastic processes for contour enhancement and contour completion. The solutions are given by groupconvolution with the corresponding Green...

RR Lyrae variables in Galactic globular clusters V. The case of M3 pulsators. Abstract. We use our synthetic Horizontal Branch (HB) procedure to approach the debated problem concerning the adequacy of canonical HB stellar models to account for the observed peaked distribution of RR Lyrae fundamentalised periods in the globular cluster M3. We find that by assuming a suitable bimodal mass distrib...

High order splitting schemes with complex timesteps are applied to Kolmogorov backward equations stemming from stochastic differential equations in Stratonovich form. In the setting of weighted spaces, the necessary analyticity of the split semigroups can be easily proved. A numerical example from interest rate theory, the CIR2 model, is considered. The numerical results are robust for drift-do...

This paper establishes Fokker–Planck–Kolmogorov type equations for time-changed Gaussian processes. Examples include those equations for a time-changed fractional Brownian motion with time-dependent Hurst parameter and for a time-changed Ornstein–Uhlenbeck process. The timechange process considered is the inverse of either a stable subordinator or a mixture of independent stable subordinators.

We develop a general technique to prove uniqueness of solutions for Fokker– Planck equations on infinite dimensional spaces. We illustrate this method by implementing it for Fokker–Planck equations in Hilbert spaces with Kolmogorov operators with irregular coefficients and both non-degenerate or degenerate second order part. 2000 Mathematics Subject Classification AMS: 60H15, 60J35, 60J60, 47D07