We discuss stochastic representations of advection diffusion equations with variable diffusivity, stochastic integrals of motion and generalized relative entropies.

We consider a class of non-homogeneous Markov chains arising in simulated annealing and related stochastic search algorithms. Using only elementary first principles, we analyze the convergence and rate of convergence of the relative frequencies of visits to states in the Markov chain. We describe in detail three examples, including the standard simulated annealing algorithm, to show how our fra...

In this paper, we derive the exact analytical expressions for the Shannon entropy of generalized orderstatistics from Pareto-type and related distributions.

The dual generalized order statistics is a unified model which contains the well known decreasingly ordered random data such as (reversed ordered) order statistics and lower record values. In the present paper, some characterization results on the power function distribution based on the properties of dual generalized order statistics are provided. The results are proved without any rest...

We provide a stochastic interpretation of a result of decay of generalized relative entropies that was discovered by Michel, Mischler and Perthame

We have considered one parametric generalization of the nonsymmetric relative J-divergence measure. The generalized measure is shown belonging to the Csiszár’s f-divergence class. Further, we have derived bounds for the generalized measure in terms of well known divergence measures.

This paper gives necessary and sufficient conditions for the (n-dimensional) generalized free rigid body to be in a state of relative equilibrium. The conditions generalize those for the case of the three-dimensional free rigid body, namely that the body is in relative equilibrium if and only if its angular velocity and angular momentum align, that is, if the body rotates about one of its princ...

We have space here to give only the briefest outline of the processes we are trying to model; the interested reader should consult one of the standard textS2. The heart consists of four chambers: two atria and two ventricles . Electrically, however, the two atria can be considered as one, and we shall refer only to the atrium ; likewise for the two ventricles. In essence the function of the car...