Related papers: Limit laws for functionals of self-intersection sy…
In the present paper, we characterize the behavior of supercritical branching processes in random environment with linear fractional offspring distributions, conditioned on having small, but positive values at some large generation. As it…
Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or weakens moment assumptions. In this paper we present several…
In this paper, we extend the central limit theorem of the additive functional of the nearest-neighbor zero-range process given in \cite{Quastel2002} to the long-range case. Our main results show that in several cases the limit processes are…
In this paper we study the conditional limit theorems for critical continuous-state branching processes with branching mechanism $\psi(\lambda)=\lambda^{1+\alpha}L(1/\lambda)$ where $\alpha\in [0,1]$ and $L$ is slowly varying at $\infty$.…
We extend a functional limit theorem for symmetric $U$-statistics [Miller and Sen, 1972] to asymmetric $U$-statistics, and use this to show some renewal theory results for asymmetric $U$-statistics. Some applications are given.
We obtain explicit criteria for both exponential ergodicity and strong ergodicity for one-dimensional time-changed symmetric stable processes with $\alpha\in(1,2)$. Explicit lower bounds for ergodic convergence rates are given.
We derive the asymptotic behavior for an additive functional of two independent self-similar Gaussian processes when their intersection local time exists, using the method of moments.
In this paper, we establish a joint (bivariate) functional central limit theorem of the sample quantile and the $r$-th absolute centred sample moment for functionals of mixing processes. More precisely, we consider $L_2$-near epoch…
We present a stability analysis framework for the general class of discrete-time linear switching systems for which the switching sequences belong to a regular language. They admit arbitrary switching systems as special cases. Using recent…
This paper provides a first example of constructing Lyapunov functions in a class of piecewise linear systems with limit cycles. The method of construction helps analyze and control complex oscillating systems through novel geometric means.…
For a stable process, we give an explicit formula for the potential measure of the process killed outside a bounded interval and the joint law of the overshoot, undershoot and undershoot from the maximum at exit from a bounded interval. We…
Let $\left\{ S_{n},n\geq 0\right\} $ be a random walk whose increment distribution belongs without centering to the domain of attraction of an $% \alpha $-stable law, i.e., there are some scaling constants $a_{n}$ such that the sequence…
Using the framework of random walks in random scenery, Cohen and Samorodnitsky (2006) introduced a family of symmetric $\alpha$-stable motions called local time fractional stable motions. When $\alpha=2$, these processes are precisely…
We give functional laws of large numbers for a class of marked Hawkes processes and marked compound Hawkes processes with a general mark space. Our results provide some complement to those presented previously in the literature. As an…
We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…
A self-stabilizing processes $\{Z(t), t\in [t_0,t_1)\}$ is a random process which when localized, that is scaled to a fine limit near a given $t\in [t_0,t_1)$, has the distribution of an $\alpha(Z(t))$-stable process, where $\alpha:…
Let $\{B_{t}\}_{t\geq0}$ be a $d$-dimensional fractional Brownian motion with Hurst parameter $0<H<1$, where $d\geq2$. Consider the approximation of the self-intersection local time of $B$, defined as \begin{align*} I_{T}^{\varepsilon}…
We give a partly new proof of the fluctuation bounds for the second class particle and current in the stationary asymmetric simple exclusion process. One novelty is a coupling that preserves the ordering of second class particles in two…
This study investigates the existence and stability of limit cycles resulting from self-excited oscillations in linear multi-degree-of-freedom systems subjected to discontinuous, state-dependent forcing. Using the method of averaging and…
Recently, for the joint partial sum and partial maxima processes constructed from linear processes with independent identically distributed innovations that are regularly varying with tail index $\alpha \in (0, 2)$, a functional limit…