Conditional expected values in Markov chains are solutions to a set of backward differential equations, which may be ordinary or partial depending on the number of relevant state variables. This paper investigates the validity of these differential equations by locating the points of...

In this paper, we are concerned with an elliptic problem in a bounded two-dimensional domain equipped with a non-linear Newton boundary condition. This problem appears, e.g. in the modelling of electrolysis procedures. We assume that the non-linearity has a polynomial behaviour. The problem is...

We present a simple method to construct approximate analytical solutions of a class of non-linear dynamical mappings in Rd(d=1,2,…). This class is defined as a system of d non-linear first-order difference equations. This system is a discrete analogue of a system of d-first-order ordinary...

We consider the moment equations for a kinetic model describing the interaction of monochromatic photons with gas-particles endowed with two internal energy levels. In the space-homogeneous case the stability of the equilibrium solution is analytically proven and numerically tested. In the...

The dynamical characteristics of continuous-time additive Hopfield-type neural networks are studied. Sufficient conditions are obtained for exponentially stable encoding of temporally uniform external stimuli. Discrete-time analogues of the corresponding continuous-time models are formulated and...

A Boltzmann-like model for the description of processes of outgassing and contamination is proposed. The cavity /oR2, where the contaminants migrate during their motion from the source region /oR1 to the target /oR3, contains a random medium.

In this paper we analyze a discretized version of the dynamic programming algorithm for a parameterized family of infinite-horizon economic models, and derive error bounds for the approximate value and policy functions. If h is the mesh size of the discretization, then the approximation error...

The permanent income hypothesis under certainty equivalence implies that optimal consumption is more volatile than labour income, when labour income is positively autocorrelated in first differences. Empirically, certainty equivalence is rejected because observed consumption is excessively...