Approximations for interactive Markov chains in discrete and continuous time

A class of models called interactive Markov chains is studied in both discrete and continuous time. These models were introduced by Conlisk and serve as a rich class for sociological modeling, because they allow for interactions among individuals. In discrete time, it is proved that the Markovian processes converge to a deterministic process almost surely as the population size becomes infinite. More importantly, the normalized process is shown to be asymptotically normal with specified mean vector and covariance matrix. In continuous time, the chain is shown to converge weakly to a diffusion process with specified drift and scale terms. The distributional results will allow for the construction of a likelihood function from interactive Markov chain data, so these results will be important for questions of statistical inference. An example from manpower planning is given which indicates the use of this theory in constructing and evaluating control policies for certain social systems.     

Statistical analysis of hierarchical stochastic models: Examples and approaches

This paper introduces and illustrates the concept of hierarchical or random parameter stochastic process models. These models arise when members of a population each generate a stochastic process governed by certain parameters and the values of the parameters may be viewed as single realizations of random variables. The paper treats the estimation of the individual parameter values and the parameters of the superpopulation distribution. Examples from system reliability, pharmacokinetic compartment models, and criminal careers are introduced; a reliability (Poisson process-exponential interval) process is examined in greater detail. An explicit, approximate, robust estimator of individual (log) failure rates is presented for the case of a long-tailed (Studentt) superpopulation. This estimator exhibits desirable limited shrinkage properties, refusing to borrow unjustified strength. Numerical properties of such estimators are described more fully elsewhere.     

Mathematical analysis of the Miller-Modigliani theory

This paper provides a rigorous mathematical treatment of the problem of valuation of a firm in a deterministic, partial equilibrium framework. It is shown that the dividend and arbitrage approaches to valuation are not equivalent in general. A necessary and sufficient condition for their equivalence is also obtained.     

Study of structural and electronic transport properties of Ce-doped LaMnO3

The structural and electronic transport properties of La_1−x Ce _x MnO₃ (x=0.0–1.0) have been studied. All the samples exhibit orthorhombic crystal symmetry and the unit cell volume decreases with Ce doping. They also make a metal-insulator transition (MIT) and transition temperature increases with increase in Ce concentration up to 50% doping. The system La_0.5Ce_0.5MnO₃ also exhibits MIT instead of charge-ordered state as observed in the hole doped systems of the same composition.     

Two connected inverse spectral transforms

We establish a transformation which connects the potentials of the one-dimensional Dirac and Klein-Gordon operators. This transformation links the solutions of the nonlinear evolution equations solvable by means of the two inverse spectral transforms which use the Dirac and Klein-Gordon direct and inverse spectral problems.