相关论文: Stationarity and ergodicity for an affine two fact…

Rotations on the circle by irrational numbers give rise to uniquely ergodic Sturm dynamical systems. We show that rotations by badly approximable irrationals have the property of fast ergodicity. It was shown recently that any Sturmian…

The higher dimensional autoregressive models would describe some of the econometric processes relatively generically if they incorporate the heterogeneity in dependence on times. This paper analyzes the stationarity of an autoregressive…

We propose an extension of ergodic theory which focuses on the identification of ergodicity in terms of the uniqueness of the invariant measure. We first explain the concept for the doubling maps, which can be analyzed using Fourier…

We study stability of the eigenvalues of the generator of a one dimensional reversible diffusion process satisfying some natural conditions. The proof is based on Stein's method. In particular, these results are applied to the Normal…

We define a de Bruijn process with parameters n and L as a certain continuous-time Markov chain on the de Bruijn graph with words of length L over an n-letter alphabet as vertices. We determine explicitly its steady state distribution and…

The work deals with establishing the solvability of a system of integro-differential equations in the situation of the double scale anomalous diffusion. Each equation of such system involves the sum of the two negative Laplace operators…

We revisit affine diffusion processes on general and on the canonical state space in particular. A detailed study of theoretic and applied aspects of this class of Markov processes is given. In particular, we derive admissibility conditions…

In this note, we discuss the uniform ergodicity of a diffusion process given by an It\^o stochastic differential equation. We present an integral condition in terms of the drift and diffusion coefficients that ensures the uniform ergodicity…

We find that in "two-photon"-like processes in the scalar $\varphi^3_E$ model and also in hadron-pair production arising from the collisions of a real (transversely polarized) and a highly virtual, longitudinally polarized, photon in QCD,…

This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic…

In this paper we obtain two criteria of stable ergodicity outside the partially hyperbolic scenario. In both criteria, we use a weak form of hyperbolicity called chain-hyperbolicity. It is obtained one criterion for diffeomorphisms with…

Front propagation in two dimensional steady and unsteady cellular flows is investigated in the limit of very fast reaction and sharp front, i.e., in the geometrical optics limit. In the steady case, by means of a simplified model, we…

Affine jump-diffusions constitute a large class of continuous-time stochastic models that are particularly popular in finance and economics due to their analytical tractability. Methods for parameter estimation for such processes require…

In this work, we investigate the fine regularity of L\'evy processes using the 2-microlocal formalism. This framework allows us to refine the multifractal spectrum determined by Jaffard and, in addition, study the oscillating singularities…

Given a domain G, a reflection vector field d(.) on the boundary of G, and drift and dispersion coefficients b(.) and \sigma(.), let L be the usual second-order elliptic operator associated with b(.) and \sigma(.). Under suitable…

The Volterra square-root process on $\mathbb{R}_+^m$ is an affine Volterra process with continuous sample paths. Under a suitable integrability condition on the resolvent of the second kind associated with the Volterra convolution kernel,…

We discuss duality in ``two-photon''-like processes in the scalar $\varphi^3_E$ model and also in the process $\gamma^*\gamma\to\pi\pi$ in QCD. Duality implies the equivalence between two distinct nonperturbative mechanisms. These two…

We study a one-dimensional stochastic differential equation driven by a stable L\'evy process of order $\alpha$ with drift and diffusion coefficients $b,\sigma$. When $\alpha\in (1,2)$, we investigate pathwise uniqueness for this equation.…

We show that for two afii varieties over an arbitrary field of characteristic zero, there is no general form of an algorithm for checking the presence of an embedding of one algebraic variety in another. Moreover, we establish this for…

Consider a one-dimensional diffusion process which has state-dependent drift and deviation and is reflected at the origin, which is called a one-side reflected diffusion or simply reflected diffusion. We are particularly interested in the…