Homogeneous Markov System Research Articles

The continuous-time homogeneous Markov system with fixed size as a Newtonian fluid

Given the velocity field of a continuous-time homogeneous Markov system (HMS) with fixed size, it is examined if the system could be considered as a continuum. The model examined is that of a Newtonian fluid. The set of attainable structures is the continuum and its evolution in Euclidean space corresponds to the motion of the continuum. It is proved that the Newtonian fluid assumption cannot generally explain the motion of the HMS. If it is possible, then we come to the conclusion that the ‘viscosity’ is a function of density and position. The dependence of viscosity on position implies that a fluid conforming to the HMS cannot be real. © 1998 John Wiley & Sons, Ltd.

The continuous‐time homogeneous Markov system with fixed size as a Newtonian fluid

The continuous‐time homogeneous Markov system with fixed size as a Newtonian fluid

The evolution of the attainable structures of a continuous time homogeneous Markov system with fixed size

In order to describe the evolution of the attainable structures of a continuous time homogeneous Markov system (HMS) with fixed size, we evaluate the volume of the sets of the attainable structures in Euclidean space in the course of time, and we find the value of the volume asymptotically. Then, using the concept of the volume of the attainable structures, we provide a method to evaluate the ‘age' of the system in continuous and discrete time. We also estimate the evolution of the distance of two (attainable) structures of the system as it changes following the transformations of the structures.

The evolution of the attainable structures of a continuous time homogeneous Markov system with fixed size

In order to describe the evolution of the attainable structures of a continuous time homogeneous Markov system (HMS) with fixed size, we evaluate the volume of the sets of the attainable structures in Euclidean space in the course of time, and we find the value of the volume asymptotically. Then, using the concept of the volume of the attainable structures, we provide a method to evaluate the ‘age' of the system in continuous and discrete time. We also estimate the evolution of the distance of two (attainable) structures of the system as it changes following the transformations of the structures.

The evolution of the attainable structures of a homogeneous Markov system by fixed size

In order to describe the evolution of the attainable structures of a homogeneous Markov system (HMS) with fixed size, we evaluate the volume of the sets of the attainable structures in Euclidean space as they are changing in time and we find the value of the volume asymptotically. We also estimate the evolution of the distance of two (attainable) structures of the system as it changes following the transformations of the structures; extensions are obtained concerning results from the Perron–Frobenius theory referring to Markov systems.

The evolution of the attainable structures of a homogeneous Markov system by fixed size

In order to describe the evolution of the attainable structures of a homogeneous Markov system (HMS) with fixed size, we evaluate the volume of the sets of the attainable structures in Euclidean space as they are changing in time and we find the value of the volume asymptotically. We also estimate the evolution of the distance of two (attainable) structures of the system as it changes following the transformations of the structures; extensions are obtained concerning results from the Perron–Frobenius theory referring to Markov systems.

Stochastic control in non‐ homogeneous markov systems

We study the problem of maintainability of the structure in a non‐homogeneous Markov ystem (NHMS) by input control. The set of maintainable structures is given as the convex hull of n‐points in Rn where n is the number of states of the NHMS. We also study the problem of attainability in a NHMS by input control and an algorithm is provided for the optimal policy in this respect. Finally, we provide applications of the present results to a large British firm

Parallel composition and decomposition of finite homogeneous Markov systems

Parallel composition and decomposition of finite homogeneous Markov systems