Related papers: Perturbation analysis of Markov modulated fluid mo…

In a previous paper (J. Phys. A 36, 11807 (2003)), we introduced the `asymptotic iteration method' for solving second-order homogeneous linear differential equations. In this paper, we study perturbed problems in quantum mechanics and we…

We study perturbation theory and uniform ergodicity for discrete-time Markov chains on general state spaces in terms of the uniform moments of the first hitting times on some set. The methods we adopt are different from previous ones. For…

We introduce a perturbative method to calculate all moments of the first-passage time distribution in stochastic one-dimensional processes which are subject to both white and coloured noise. This class of non-Markovian processes is at the…

We propose an improved scheme of perturbation theory based on our exact solution [An Min Wang, quant-ph/0611216] in general quantum systems independent of time. Our elementary start-point is to introduce the perturbing parameter as late as…

We report lowest-order series expansions for primary matrix functions of quantum states based on a perturbation theory for functions of linear operators. Our theory enables efficient computation of functions of perturbed quantum states that…

We consider the survival probability of a particle in the presence of a finite number of diffusing traps in one dimension. Since the general solution for this quantity is not known when the number of traps is greater than two, we devise a…

We study an ensemble of random matrices (the Rosenzweig-Porter model) which, in contrast to the standard Gaussian ensemble, is not invariant under changes of basis. We show that a rather complete understanding of its level correlations can…

A popular method to compute first-passage probabilities in continuous-time Markov chains is by numerically inverting their Laplace transforms. Past decades, the scientific computing community has developed excellent numerical methods for…

First-passage properties are central to the kinetics of target-search processes. Theoretical approaches so far primarily focused on predicting first-passage statistics for a given process or model. In practice, however, one faces the…

We provide a dynamical study of a model of multiplicative perturbation of a unitary matrix introduced by Fyodorov. In particular, we identify a flow of deterministic domains that bound the spectrum with high probability, separating the…

We consider the filtering of continuous-time finite-state hidden Markov models, where the rate and observation matrices depend on unknown time-dependent parameters, for which no prior or stochastic model is available. We quantify and…

We construct a stochastic fluid process with an underlying piecewise deterministic Markov process (PDMP) akin to the one used in the construction of the rational arrival process (RAP), which we call the RAP-modulated fluid process. As…

We investigate the curvature perturbations induced by the randomness of the quantum tunneling process during cosmological first-order phase transitions (PTs) and for the first time ultilize curvature perturbations to constrain the PT…

We consider the eigenvalues and eigenvectors of finite, low rank perturbations of random matrices. Specifically, we prove almost sure convergence of the extreme eigenvalues and appropriate projections of the corresponding eigenvectors of…

The effects of the resonant magnetic perturbations (RMPs) on the turbulent transport are analyzed in the framework of the test particle approach using a semi-analytical method. The normalized RMP amplitude $P_{b}$ extends on a large range,…

We study the growth of structures in modified gravity models where the Poisson equation and the relationship between the two Newtonian potentials are modified by explicit functions of space and time. This parameterisation applies to the…

Given a unichain Markov reward process (MRP), we provide an explicit expression for the bias values in terms of mean first passage times. This result implies a generalization of known Markov chain perturbation bounds for the stationary…

We characterize Markov lattice semigroups induced by measurable semiflows on probability spaces by properties of their generators. In addition we construct topological models on compact spaces for such semigroups.

In this paper the problems of the retrospective analysis of models with time-varying structure are considered. These models include contamination models with randomly switching parameters and multivariate classification models with an…

We consider the long-time behavior of systems close to a system with a smooth first integral. Under certain assumptions, the limiting behavior, to some extent, turns out to be universal: it is determined by the first integral, the…