Published in Israel Journal of Mathematics
LetX1 andX2 be two mixing Markov shifts over finite alphabet. If the entropy ofX1 is strictly larger than the entropy ofX2, then there exists a finitary homomorphism ϕ:X1→X2 such that the code length is anLp random variable for allp
Published in Annals of Operations Research
This paper models and analyzes multi‐stage transfer lines with unreliable machines and finite buffers. The machines have exponential operation, failure, and repair processes. First, a mixed vector–scalar Markov process model is presented based on some notations of mixed vector–scalar operations. Then, several steady‐state system properties are dedu...
Published in Ukrainian Mathematical Journal
Published in Radiophysics and Quantum Electronics
Using the method of generative processes, we construct a model of a random linear symmetric stable Markov process, which is a natural generalization of the Markov Gaussian process and preserves its main property: invariance with respect to arbitrary linear transformations. Methods for analyzing such processes are developed. In particular, it is pro...
Published in Ukrainian Mathematical Journal
We describe a (B, S,X )-incomplete market of securities with jumps as a jump random evolution process that is a combination of an ltô process in random Markov medium and a geometric compound Poisson process. For this model, we derive the Black-Scholes equation and formula, which describe the pricing of the European call option under conditions of (...
Published in Probability Theory and Related Fields
Let X be a symmetric stable process of index α∈ (1,2] and let Lxt denote the local time at time t and position x. Let V(t) be such that LtV(t) = supx∈ℝLtx. We call V(t) the most visited site of X up to time t. We prove the transience of V, that is, limt→∞ |V(t)| = ∞ almost surely. An estimate is given concerning the rate of escape of V. The result ...
Published in Theoretical and Mathematical Physics
The evolution of a system with phase transition is simulated by a Markov process whose transition probabilities depend on a parameter. The change of the stationary distribution of the Markov process with a change of this parameter is interpreted as a phase transition of the system from one thermodynamic equilibrium state to another. Calculations an...
Published in IIE Transactions
This paper develops two algorithms for computing the average total cost per product and other performance measures for a make-to-order inventory-production system. The two algorithms are developed by using matrix analytic methods. The first algorithm is based on the matrix-geometric solution of the Quasi-Birth-and-Death (QBD) Markov process. The se...
Published in Open Systems & Information Dynamics
There has been some opposition to the use of Markov processes in quantum mechanics based upon the fact that no quantum mechanical regression principle can be applied. It is argued here however that one may just as well conclude that there is no classical mechanical regression principal either. The dissipative component of a canonical stochastic flo...
Published in Ukrainian Mathematical Journal
We prove that the amplitudes and the phases of eigenoscillations of a linear oscillating system perturbed by either a fast Markov process or a small Wiener process can be described asymptotically as a diffusion process whose generator is calculated.
