Related papers: A renewal theorem for relatively stable variables

We revisit strong approximation theory from a new perspective, culminating in a proof of the Koml\'os-Major-Tusn\'ady embedding theorem for the simple random walk. The proof is almost entirely based on a series of soft arguments and easy…

We consider random variables observed at arrival times of a renewal process, which possibly depends on those observations and has regularly varying steps with infinite mean. Due to the dependence and heavy tailed steps, the limiting…

We identify a single computationally checkable analytic quantity interlacing Martin boundary collapse, Green geometry, and linear escape for transient random walks on finitely generated groups: the Green-variation functional \[…

In this paper, we discuss long-time behavior of sample paths for a wide range of regime-switching diffusions. Firstly, almost sure asymptotic stability is concerned (i) for regime-switching diffusions with finite state spaces by the…

A regenerative composition structure is a sequence of ordered partitions derived from the range of a subordinator by a natural sampling procedure. In this paper, we extend previous studies Barbour and Gnedin (2006), Gnedin, Iksanov and…

Two new test statistics are introduced to test the null hypotheses that the sampling distribution has an increasing hazard rate on a specified interval [0,a]. These statistics are empirical L_1-type distances between the isotonic estimates,…

We consider in this paper subdiffusion in a system with a thin membrane. The subdiffusion parameters are the same in both parts of the system separated by the membrane. Using the random walk model with discrete time and space variables the…

The generalized entropic measure, which is optimized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity, is considered and its…

We construct a renewal structure for random walks on surface groups. The renewal times are defined as times when the random walks enters a particular type of a cone and never leaves it again. As a consequence, the trajectory of the random…

We study the random walk $(S_n)_{n\geq 1}$ with independent and identically distributed real-valued increments having zero mean and an absolute moment of order $2 + \delta$ for some $\delta > 0$. For any starting point $x \in \mathbb{R}$,…

In this paper, we study random walks $g_n=f_{n-1}\cdots f_0$ on the group $\mathrm{Homeo}(S^1)$ of the homeomorphisms of the circle, where the homeomorphisms $f_k$ are chosen randomly, independently, with respect to a same probability…

Let $(X,\mathcal{F},\mu,T)$ be a not necessarily invertible non-atomic measure-preserving dynamical system where the $\sigma$-algebra $\mathcal{F}$ is generated by the intervals according to some total order. The main result is that the…

The main result of this paper is a general central limit theorem for distributions defined by certain renewal type equations. We apply this to weakly self-avoiding random walks. We give good error estimates and Gaussian tail estimates which…

We study equilibrium selection for invariant measures of stochastic dynamical systems with constant step size, under persistent noise and minimal moment assumptions, in a general quasi-Feller framework. Such dynamics arise in…

Let $G$ be a real Lie group, $\Lambda<G$ a lattice and $H<G$ a connected semisimple subgroup without compact factors and with finite center. We define the notion of $H$-expanding measures $\mu$ on $H$ and, applying recent work of…

Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…

We show that if a numerical method is posed as a sequence of operators acting on data and depending on a parameter, typically a measure of the size of discretization, then consistency, convergence and stability can be related by a…

We study a scenario under which variable step random walks give anomalous statistics. We begin by analyzing the Martingale Central Limit Theorem to find a sufficient condition for the limit distribution to be non-Gaussian. We note that the…

We consider a dynamical system with state space $M$, a smooth, compact subset of some ${\Bbb R}^n$, and evolution given by $T_t$, $x_t = T_t x$, $x \in M$; $T_t$ is invertible and the time $t$ may be discrete, $t \in {\Bbb Z}$, $T_t = T^t$,…

We prove existence of asymptotic entropy of random walks on regular languages over a finite alphabet and we give formulas for it. Furthermore, we show that the entropy varies real-analytically in terms of probability measures of constant…