相关论文: Counterexample to a theorem on quasi-birth-and-dea…

Given a birth-death process on $\mathbb {N}$ with semigroup $(P_t)_{t\geq0}$ and a discrete gradient ${\partial}_u$ depending on a positive weight $u$, we establish intertwining relations of the form ${\partial}_uP_t=Q_t\,{\partial}_u$,…

The aim of this paper is to study the asymptotic behavior of a system of birth and death processes in mean field type interaction in discrete space. We first establish the exponential convergence of the particle system to equilibrium for a…

An elementary proof is given for a theorem showing that certain birth-death chains show martingale-like behavior at large stopping times. This is a generalization of and new proof for a theorem from a earlier paper by the author.

We consider a pure death process $(Z(t), t\ge0)$ with death rates $\lambda_n$ satisfying the condition $\sum_{n=2}^\infty \lambda_n^{-1}<\infty$ of coming from infinity, $Z(0)=\infty$, down to an absorbing state $n=1$. We establish limit…

Counterexample models to the Nelson-Seiberg theorem have been discovered, and their features have been studied in previous literature. All currently known counterexamples have generic superpotentials respecting the R-symmetry, and more…

The birth-death process is a special type of continuous-time Markov chain with index set $\mathbb{N}$. Its resolvent matrix can be fully characterized by a set of parameters $(\gamma, \beta, \nu)$, where $\gamma$ and $\beta$ are…

We study a fractional birth-death process with state dependent birth and death rates. It is defined using a system of fractional differential equations that generalizes the classical birth-death process introduced by Feller (1939). We…

The author cannot grant that Quantum Mechanics satisfies the axioms described here when repeated measurements are at stake. This does not compromise the validity of the conclusions of the previous article "A glance beyond the quantum…

Csiszar's f-divergence of two probability distributions was extended to the quantum case by the author in 1985. In the quantum setting positive semidefinite matrices are in the place of probability distributions and the quantum…

Let $\omega=(\omega_i)_{i\in\mathbb Z}=(\mu^{L}_i,...,\mu^{1}_i,\lambda_i)_{i\in \mathbb Z}$, which serves as the environment, be a sequence of i.i.d. random nonnegative vectors, with $L\ge1$ a positive integer. We study birth and death…

By providing instances of approximation of linear diffusions by birth-death processes, Feller [13], has offered an original path from the discrete world to the continuous one. In this paper, by identifying an intertwining relationship…

In this paper I shall give the complete solution of the equations governing the bilateral birth and death process on path set $\mathbb{R}_q=\{q^n,\quad n\in\mathbb{Z}\}$ in which the birth and death rates $\lambda_n=q^{2\nu-2n}$ and…

This paper has been withdrawn by the author; a revised version is part of the author's phd-thesis "Quasi-logarithmic structures" (Zurich, 2007).

In a recent article [Phys. Rev. A 94, 052128 (2016)], the authors compute the predictions of two collapse models on the transition probabilities of neutral mesons. Notably, they claim to find an influence on the decay rates and attempt to…

In this short note we give counterexamples to several results related to extension theorems published recently.

We develop a likelihood-based inference for finite-state birth-death processes with composite birth rates, in which multiple distinct mechanisms contribute additively to the total birth intensity. Our main motivating example is an SIS…

We consider the following variant of the Mortality Problem: given $k\times k$ matrices $A_1, A_2, \dots,A_{t}$, does there exist nonnegative integers $m_1, m_2, \dots,m_t$ such that the product $A_1^{m_1} A_2^{m_2} \cdots A_{t}^{m_{t}}$ is…

By using the quasi-determinant the construction of Gel'fand et al. leads to the inverse of a matrix with noncommuting entries. In this work we offer a new method that is more suitable for physical purposes and motivated by deformation…

In this short note we show, providing counterexamples, that the "two important theorems" in the recent paper [Y, Yuan, Global optimization solutions to a class of non-convex quadratic minimization problems with quadratic constraints, in…

We consider models of the population or opinion dynamics which result in the non-linear stochastic differential equations (SDEs) exhibiting the spurious long-range memory. In this context, the correspondence between the description of the…