Adaptive Control of a Partially Observed Discrete Time Markov Process

An adaptive control problem of a discrete time Markov process that is completely observed in a fixed recurrent domain and is partially observed elsewhere is formulated and a solution is given by constructing an approximately self-optimal strategy. The state space of the Markov process is either a closed subset of Euclidean space or a countable set. Another adaptive control problem is solved where the process is always only partially observed but there is a family of random times when the process evaluated at these times is a family of independent, identically distributed random variables. Accepted 26 April 1996     

On some problems arising in asymptotic analysis of Markov processes with singularly perturbed generators

In, the paper we study singularly perturbed Markov processes. Some new results in convergence of resolvents, weak convergence and convergence of semigroups are obtained. The results are applied to optima1 stopping and impulse control of singular1y perturbed Markov processes. Examples justifying the assumptions made in text are also presented     

In situ surface x-ray diffraction studies of homoepitaxial electrochemical growth on Au(100)

Direct in situ x-ray surface scattering studies of growth at a solid-liquid interface are demonstrated using the homoepitaxial electrodeposition on Au(100) as an example. With decreasing potential transitions from step-flow to layer-by-layer growth, manifested by layering oscillations in the x-ray intensity, then to multilayer growth, and finally back to layer-by-layer growth were observed. This complex growth behavior can be explained by the effect of anion coadsorbates and the potential-dependent Au surface reconstruction on the Au surface mobility.     

A note on chaotic and predictable representations for Itô–Markov additive processes

In this article, we provide predictable and chaotic representations for Itô–Markov additive processes X. Such a process is governed by a finite-state continuous time Markov chain J which allows one to modify the parameters of the Itô-jump process (in so-called regime switching manner). In addition, the transition of J triggers the jump of X distributed depending on the states of J just prior to the transition. This family of processes includes Markov modulated Itô–Lévy processes and Markov additive processes. The derived chaotic representation of a square-integrable random variable is given as a sum of stochastic integrals with respect to some explicitly constructed orthogonal martingales. We identify the predictable representation of a square-integrable martingale as a sum of stochastic integrals of predictable processes with respect to Brownian motion and power-jumps martingales related to all the jumps appearing in the model. This result generalizes the seminal result of Jacod–Yor and is of importance in financial mathematics. The derived representation then allows one to enlarge the incomplete market by a series of power-jump assets and to price all market-derivatives.     

Structure and electrocompression of chloride adlayers on Cu(111)

The specific adsorption of chloride on Cu(111) from acidic aqueous electrolyte (pH 3) was investigated by in-situ surface X-ray diffraction, revealing an incommensurate hexagonal rotated adlayer. The structure and its potential dependence suggest a strong adsorbate–adsorbate interaction as compared to other halide adlayers on (111)-oriented metal electrode surfaces. The orientational epitaxy can be rationalized by the model suggested by Grey and Bohr (Europhys. Lett. 18, 171, 1992), which is based on symmetry considerations.     

A novel X‐ray diffractometer for studies of liquid–liquid interfaces

The study of liquid–liquid interfaces with X‐ray scattering methods requires special instrumental considerations. A dedicated liquid surface diffractometer employing a tilting double‐crystal monochromator in Bragg geometry has been designed. This diffractometer allows reflectivity and grazing‐incidence scattering measurements of an immobile mechanically completely decoupled liquid sample, providing high mechanical stability. The available energy range is from 6.4 to 29.4 keV, covering many important absorption edges. The instrument provides access in momentum space out to 2.54 Å^?1 in the surface normal and out to 14.8 Å^?1 in the in‐plane direction at 29.4 keV. Owing to its modular design the diffractometer is also suitable for heavy apparatus such as vacuum chambers. The instrument performance is described and examples of X‐ray reflectivity studies performed under in situ electrochemical control and on biochemical model systems are given.     

Ergodic Control of a Singularly Perturbed Markov Process in Discrete Time with General State and Compact Action Spaces

Ergodic control of singularly perturbed Markov chains with general state and compact action spaces is considered. A new method is given for characterization of the limit of invariant measures, for perturbed chains, when the perturbation parameter goes to zero. It is also demonstrated that the limit control principle is satisfied under natural ergodicity assumptions about controlled Markov chains. These assumptions allow for the presence of transient states, a situation that has not been considered in the literature before in the context of control of singularly perturbed Markov processes with long-run-average cost functionals. Accepted 3 December 1996     

Growth Optimal Portfolio Selection Under Proportional Transaction Costs with Obligatory Diversification

A continuous time long run growth optimal or optimal logarithmic utility portfolio with proportional transaction costs consisting of a fixed proportional cost and a cost proportional to the volume of transaction is considered. The asset prices are modeled as exponent of diffusion with jumps whose parameters depend on a finite state Markov process of economic factors. An obligatory portfolio diversification is introduced, accordingly to which it is required to invest at least a fixed small portion of our wealth in each asset.