No cut-off phenomenon for the “Insect Markov chain”

In this work we show that the probability measure associated with the Insect Markov chain defined on the ultrametric space of the leaves of the q-ary rooted tree of depth n ≥ 2 converges to the stationary distribution without a cut-off behavior.     

A Markov chain model for Asch‐type experiments†

A 4‐state absorbing Markov chain is advanced as a model to represent the response process of subjects in Asch‐type experiments. Both the development of the model and the estimation of its parameters are described. The model is applied to the responses obtained from subjects in an Asch‐type experiment designed to analyze the effects of prior status expectations on social influence.     

A simple explanation for the “shuffling phenomenon” for lozenge tilings of dented hexagons

In a recent preprint, Lai and Rohatgi proved a “shuffling theorem” for lozenge tilings of a hexagon with “dents” (i.e., missing triangles). Here, we shall point out that this follows immediately from the enumeration of Gelfand–Tsetlin patterns with given bottom row. This observation is also contained in a recent preprint of Byun.     

Exact asymptotics for the stationary distribution of a Markov chain: a production model

We derive rough and exact asymptotic expressions for the stationary distribution π of a Markov chain arising in a queueing/production context. The approach we develop can also handle “cascades,” which are situations where the fluid limit of the large deviation path from the origin to the increasingly rare event is nonlinear. Our approach considers a process that starts at the rare event. In our production example, we can have two sequences of states that asymptotically lie on the same line, yet π has different asymptotics on the two sequences.     

When the “Bull” Meets the “Bear”—A First Passage Time Problem for a Hidden Markov Process

Let _t be a continuous Markov chain on N states. Consider adjoining a Brownian motion with this Markov chain so that the drift and the variance take different values when _t is in different states. This new process Z_t is a hidden Markov process. We study the probability distribution of the first passage time for Z_t.Our result, when applied to the stock market, provides an explicit mathematical interpretation of the fact that in finite time, there is positive probability for the bull (bear) market to become bear (bull).     

A Padé-based algorithm for overcoming the Gibbs phenomenon

Truncated Fourier series and trigonometric interpolants converge slowly for functions with jumps in value or derivatives. The standard Fourier–Padé approximation, which is known to improve on the convergence of partial summation in the case of periodic, globally analytic functions, is here extended to functions with jumps. The resulting methods (given either expansion coefficients or function values) exhibit exponential convergence globally for piecewise analytic functions when the jump location(s) are known. Implementation requires just the solution of a linear system, as in standard Padé approximation. The new methods compare favorably in experiments with existing techniques.     

A Markoff-type chain for the view-obstruction problem for spheres in ℝ4

In the view-obstruction problem, congruent, closed, convex bodies centred at the points in ⁿ are expanded uniformly until they block all rays from the origin into the open positive cone. The central problem is to determine the minimal blocking size. In the case of spheres of diameter 1, this value is denoted byv(n) and is known for dimensionsn=2,3. Here we show that and obtain a Markoff type chain of isolated extreme values.     

Invariant Measure for the Markov Process Corresponding to a PDE System

In this paper, we consider the Markov process （X^∈（t）, Z^∈（t）） corresponding to a weakly coupled elliptic PDE system with a small parameter ∈ 〉 0. We first prove that （X^∈（t）, Z^∈（t）） has the Feller continuity by the coupling method, and then prove that （X^∈（t）, Z^∈（t）） has an invariant measure μ^∈（·） by the Foster-Lyapunov inequality. Finally, we establish a large deviations principle for μ^∈（·） as the small parameter e tends to zero.     

On the Empty Essential Spectrum for Markov Processes in Dimension One

This paper gives characterizations for diffusion processes on the line and birth-death processes whose generators admit the empty essential spectra. Some equivalent conditions for empty essential spectra for general Markov generators are also discussed.     

A Correction Note on: When the “Bull” Meets the “Bear”—A First Passage Time Problem for a Hidden Markov Process

Guo (Methodol Comput Appl Probab 3(2):135–143, 2001a) derived the Laplace transform of the first-passage time in a 2-state Markov-switching model and gave one of the pioneering works improving the analytical tractability of Markov-switching models. However, the Laplace transforms in her paper are wrong. This short note provides the correct expression and an alternative proof using the matrix Wiener–Hopf technique.     

Application of new treatment methods for “reading” of the complex capacitance: A quantitative description of the aging phenomenon in polymer glasses

The glassy dynamics have been investigated using electric capacitance measurements for thin films of poly(2-chlorostyrene). The observed relaxation behavior of the electric capacitance has been analyzed using a new smoothing procedure for the noisy curves and the eigen-coordinates method for the fitting trends obtained in the results of the smoothing procedure. Such analysis has given us a fascinating relaxation function related to the glassy dynamics. New aging curve will give us a chance to understand a proper physical mechanism (related to a possible formation of dynamical self-similar interacting clusters) that can describe this interesting phenomenon. Physical consequences for the recognized relaxation function are discussed.     

Large Deviations for Quantum Markov Semigroups on the 2 × 2-Matrix Algebra

Let be a predual quantum Markov semigroup acting on the full 2 × 2-matrix algebra and having an absorbing pure state. We prove that for any initial state ω, the net of orthogonal measures representing the net of states satisfies a large deviation principle in the pure state space, with a rate function given in terms of the generator, and which does not depend on ω. This implies that is faithful for all t large enough. Examples arising in weak coupling limit are studied. Submitted: January 9, 2008. Accepted: April 15, 2008.     

On the Generalized Feynman–Kac Transformation for?Nearly Symmetric Markov Processes

Suppose that X is a right process which is associated with a non-symmetric Dirichlet form $(\mathcal{E},D(\mathcal{E}))$ on L ²(E;m). For $u\in D(\mathcal{E})$ , we have Fukushima??s decomposition: $\tilde{u}(X_{t})-\tilde{u}(X_{0})=M^{u}_{t}+N^{u}_{t}$ . In this paper, we investigate the strong continuity of the generalized Feynman?CKac semigroup defined by $P^{u}_{t}f(x)=E_{x}[e^{N^{u}_{t}}f(X_{t})]$ . Let $Q^{u}(f,g)=\mathcal{E}(f,g)+\mathcal{E}(u,fg)$ for $f,g\in D(\mathcal{E})_{b}$ . Denote by J ₁ the dissymmetric part of the jumping measure J of $(\mathcal{E},D(\mathcal{E}))$ . Under the assumption that J ₁ is finite, we show that $(Q^{u},D(\mathcal{E})_{b})$ is lower semi-bounded if and only if there exists a constant ?? ₀??0 such that $\|P^{u}_{t}\|_{2}\leq e^{\alpha_{0}t}$ for every t>0. If one of these conditions holds, then $(P^{u}_{t})_{t\geq0}$ is strongly continuous on L ²(E;m). If X is equipped with a differential structure, then this result also holds without assuming that J ₁ is finite.     

Thet→∞ asymptotic regime of the Cauchy problem solution for the Toda chain with threshold-type Initial data

We obtain formulas allowing us to find solutions of the Toda chain using the inverse scattering transform method and investigate the t→∞ asymptotic behavior of the solutions. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 119, No. 3, pp. 429–440, June, 1999     

Criterion for a chain of σ-processes to be the composition of triangular chains

The purpose of this paper is to establish a topological criterion for a chain of spheres in a two-dimensional complex manifold to be a composition of so-called triangular chains. Explicit formulas are given for the relevant topological characteristics of chains. Certain corollaries of this criterion related to the Jacobian conjecture are discussed. Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 643–653, May, 1999.     

Bohr?s phenomenon for analytic functions into the exterior of a compact convex body

Bohr?s inequality for the class of analytic functions mapping the unit disk into the exterior of a compact convex body is established. In this general case, the radius obtained is . When the compact convex body is the closed unit disk, a sharp radius of 1/3 is obtained.