We provide the explicit solutions of linear, left-invariant, diffusion equations and the corresponding resolvent equations on the 2D-Euclidean motion group SE(2) = R T. These parabolic equations are forward Kolmogorov equations for well-known stochastic processes for contour enhancement and contour completion. The solutions are given by group convolution with the corresponding Green’s functions...

We provide the explicit solutions of linear, left-invariant, diffusion equations and the corresponding resolvent equations on the 2D-Euclidean motion group SE(2) = R T. These parabolic equations are forward Kolmogorov equations for well-known stochastic processes for contour enhancement and contour completion. The solutions are given by group convolution with the corresponding Green’s functions...

We consider a class of inhomogeneous birth-death queueing models and obtain uniform approximation bounds of two-sided truncations. Some examples are considered. Our approach to truncations of the state space can be used in modeling information flows related to high-performance computing. INTRODUCTION It is well known that explicit expressions for the probability characteristics of stochastic bi...

The work deals with non-Markov processes and the construction of systems differential equations delay that describe probability vectors such processes. generating stochastic operator properties operators are used to construct define

The stochastic multicloud model (SMCM) was recently developed (Khouider, Biello, and Majda, 2010) to represent the missing variability in general circulation models due to unresolved features of organized tropical convection. This research aims at finding a robust calibration methodology for the SMCM to estimate key model parameters from data. We formulate the calibration problem within a Bayes...

We consider stochastically modeled reaction networks and prove that if a constant solution to the Kolmogorov forward equation decays fast enough relative to the transition rates, then the model is non-explosive. In particular, complex balanced reaction networks are non-explosive.

We consider a non-homogeneous continuous time Markov chain model for Long-Term Care with five states: the autonomous state, three dependent states of light, moderate and severe dependence levels death state. For general approach, we allow non null intensities all returns from higher to lesser dependencies in multi-state model. Using data 2015 Portuguese National Network Continuous database, as ...

For Kolmogorov equations associated to finite dimensional stochastic differential (SDEs) in high dimension, a numerical method alternative Monte Carlo simulations is proposed. The structure of the SDE inspired by Partial Differential Equations (SPDE) and thus contains an underlying Gaussian process which key algorithm. A series development solution terms iterated integrals given, it proved conv...

In this paper we investigate the continuum limits of a class of Markov chains. The investigation of such limits is motivated by the desire to model very large networks. We show that under some conditions, a sequence of Markov chains converges in some sense to the solution of a partial differential equation. Based on such convergence we approximate Markov chains modeling networks with a large nu...