Related papers: Invariance principles for local times in regenerat…

We prove that when a sequence of L\'evy processes $X^{(n)}$ or a normed sequence of random walks $S^{(n)}$ converges a.s. on the Skorokhod space toward a L\'evy process $X$, the sequence $L^{(n)}$ of local times at the supremum of $X^{(n)}$…

Let X_{n} be an integer valued Markov Chain with finite state space. Let S_{n}=\sum_{k=0}^{n}X_{k} and let L_{n}(x) be the number of times S_{k} hits x up to step n. Define the normalized local time process t_{n}(x) by…

We study a class of Markov processes that combine local dynamics, arising from a fixed Markov process, with regenerations arising at a state-dependent rate. We give conditions under which such processes possess a given target distribution…

We investigate the connection between conditional local limit theorems and the local time of integer-valued stationary processes. We show that a conditional local limit theorem (at 0) implies the convergence of local times to Mittag-Leffler…

The subject of this paper is to prove a functional weak invariance principle for the local time of a process generated by a Gibbs-Markov map. More precisely, let $\left(X,\mathcal{B},m,T,\alpha\right)$ is a mixing, probability preserving…

We derive an invariance principle for the lift to the rough path topology of stochastic processes with delayed regenerative increments under an optimal moment condition. An interesting feature of the result is the emergence of area anomaly,…

We study a one-dimensional diffusion $X$ in a drifted Brownian potential $W\_\kappa$, with $ 0\textless{}\kappa\textless{}1$, and focus on the behavior of the local times $(\mathcal{L}(t,x),x)$ of $X$ before time $t\textgreater{}0$.In…

This article addresses a modification of local time for stochastic processes, to be referred to as `natural local time'. It is prompted by theoretical developments arising in mathematical treatments of recent experiments and observations of…

Many regenerative arguments in stochastic processes use random times which are akin to stopping times, but which are determined by the future as well as the past behaviour of the process of interest. Such arguments based on "conditioning on…

In this paper, we consider a continuous-time Markov process and prove a local limit theorem for the integral of a time-inhomogeneous function of the process. One application is in the study of the fast-oscillating perturbations of linear…

On a probability space $(\Omega,\mathcal{A},\mathbb{Q})$ we consider two filtrations $\mathbb{F}\subset \mathbb{G}$ and a $\mathbb{G}$ stopping time $\theta$ such that the $\mathbb{G}$ predictable processes coincide with $\mathbb{F}$…

We consider a renewal process with regularly varying stationary and weakly dependent steps, and prove that the steps made before a given time $t$, satisfy an interesting invariance principle. Namely, together with the age of the renewal…

We study the existence and regularity of local times for general $d$-dimensional stochastic processes. We give a general condition for their existence and regularity properties. To emphasize the contribution of our results, we show that…

Renewal theorems are developed for point processes with interarrival times $W_n=\xi(X_{n+1}X_n\cdots)$, where $(X_n)_{n\in\mathbb Z}$ is a stochastic process with finite state space $\Sigma$ and $\xi\colon\Sigma_A\to\mathbb R$ is a H\"older…

Invariance times are stopping times $\tau$ such that local martingales with respect to some reduced filtration and an equivalently changed probability measure, stopped before $\tau$ , are local martingales with respect to the original model…

We study a continuous time random walk X in an environment of dynamic random conductances. We assume that the conductances are stationary ergodic, uniformly bounded and bounded away from zero and polynomially mixing in space and time. We…

We study Markov processes conditioned so that their local time must grow slower than a prescribed function. Building upon recent work on Brownian motion with constrained local time in [5] and [33], we study transience and recurrence for a…

We study a notion of local time for a continuous path, defined as a limit of suitable discrete quantities along a general sequence of partitions of the time interval. Our approach subsumes other existing definitions and agrees with the…

We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated…

The usable limits of the customary and relaxational filtrational theories are considered. The questions of applicable the locality and local thermodynamical equilibrium principles to depict the nonstationary flows are discussed. The…