Ito’s construction of Markovian solutions to stochastic equations driven by a Lévy noise is extended to nonlinear distribution dependent integrands aiming at the effective construction of linear and nonlinear Markov semigroups and the corresponding processes with a given pseudo-differential generator. It is shown that a conditionally positive integro-differential operator (of the Lévy-Khintchin...

A new approach to multi−resolution modeling of images is introduced and applied to the task of semi−unsupervised texture segmentation using Gaussian Markov random fields (GMRFs). It is shown that traditional GMRF modeling of multi−resolution coefficients is incapable of accounting for the non−Gaussian statistics which often characterize the multi−resolution coefficients. On the other hand, the ...

In the context of nonparametric Bayesian estimation aMarkov chainMonte Carlo algorithm is devised and implemented to sample from the posterior distribution of the drift function of a continuously or discretely observed one-dimensional diffusion. The drift is modeled by a scaled linear combination of basis functions with a Gaussian prior on the coefficients. The scaling parameter is equipped wit...

Excerpted Section A. MARKOV CHAIN APPROXIMATION Another approach to finite differences is the well developed Markov Chain Approximation (MCA) of Kushner [3, 4]. Recent developments are surveyed and further advanced by Kushner [5], and by Kushner and Dupuis [6], with special attention to methods for jump and reflected diffusions. This method applies a Markov chain approximation to continuous tim...

The entropy of a binary symmetric Hidden Markov Process is calculated as an expansion in the noise parameter ǫ. We map the problem onto a one-dimensional Ising model in a large field of random signs and calculate the expansion coefficients up to second order in ǫ. Using a conjecture we extend the calculation to 11th order and discuss the convergence of the resulting series.

It is proven that the eigenvalue process of Dyson’s random matrix process of size two becomes non-Markov if the common coefficient 1/ √ 2 in the non-diagonal entries is replaced by a different positive number.

in this paper, absorbing markov chain models are developed to determine the optimum process mean levels for both a single-stage and a serial two-stage production system in which items are inspected for conformity with their specification limits. when the value of the quality characteristic of an item falls below a lower limit, the item is scrapped. if it falls above an upper limit, the item is ...

In this paper, we discuss the design, development and testing of a prototype object-oriented framework for performing supply chain simulations. We define the primary objects required for supply chain simulations and design how each of these objects are related to each other to form a supply chain network. We also present how persistence is handled for instantiating supply chain network simulati...

We present a Markov chain model of succession in a rocky subtidal community based on a long-term (1986-1994) study of subtidal invertebrates (14 species) at Ammen Rock Pinnacle in the Gulf of Maine. The model describes successional processes (disturbance, colonization, species persistence, and replacement), the equilibrium (stationary) community, and the rate of convergence. We described succes...