相关论文: Intrinsically Weighted Means of Marked Point Proce…
We consider weighted ergodic averages indexed by primes, where the weight depends on the prime, and is a "trace function" coming from algebraic geometry. We obtain extensions the classical mean-ergodic and pointwise ergodic theorems, as…
We investigate the moment estimation for an ergodic diffusion process with unknown trend coefficient. We consider nonparametric and parametric estimation. In each case, we present a lower bound for the risk and then construct an…
We study some regularity properties in locally stationary Markov models which are fundamental for controlling the bias of nonparametric kernel estimators. In particular, we provide an alternative to the standard notion of derivative process…
Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…
Weighted mean value identities over balls are considered for harmonic functions and their derivatives. Logarithmic and other weights are involved in these identities for functions. Some applications of weighted identities are presented.…
This paper relates - for point processes $\Phi$ on $\mathbb{R}$ - two types of asymptotic mean stationarity (AMS) properties and several absolute continuity results for the common probability measures emerging from point process theory. It…
We show that for a large class of marked point processes there exists a random measure m with the predictable representation property such that iterated integrals with respect to m span the space of square integrable random variables.
This paper presents a nonparametric method for estimating the conditional density associated to the jump rate of a piecewise-deterministic Markov process. In our framework, the estimation needs only one observation of the process within a…
Markov state models (MSMs) have been broadly adopted for analyzing molecular dynamics trajectories, but the approximate nature of the models that results from coarse-graining into discrete states is a long-known limitation. We show…
A point process on a space is a random bag of elements of that space. In this paper we explore programming with point processes in a monadic style. To this end we identify point processes on a space X with probability measures of bags of…
A definition of metastable states applicable to arbitrary finite state Markov processes satisfying detailed balance is discussed. In particular, we identify a crucial condition that distinguishes genuine metastable states from other types…
We prove a multidimensional ergodic theorem with weighted averages for the action of the group $\mathbb{Z}^d$ on a probability space. At level $n$ weights are of the form $n^{-d} \psi(j/n)$, $ j\in \mathbb{Z}^d$, for real functions $\psi$…
In environmental applications of extreme value statistics, the underlying stochastic process is often modeled either as a max-stable process in continuous time/space or as a process in the domain of attraction of such a max-stable process.…
A parametric point process model is developed, with modeling based on the assumption that sequential observations often share latent phenomena, while also possessing idiosyncratic effects. An alternating optimization method is proposed to…
This article concerns the estimation of hitting time statistics for potentially non-stationary processes. The main focus is exceedance times of environmental processes. To this end we consider an empirical estimator based on ergodic theory…
Ergodic optimization aims to describe dynamically invariant probability measures that maximize the integral of a given function. For a wide class of intrinsically ergodic subshifts over a finite alphabet, we show that the space of…
In this paper, we analyze the asymptotic behavior of the point process of exceedances in a spatio-temporal setting whose points are given by the rescaled occurrence times, the sites and the rescaled values of exceedances. Here, the…
As we discuss, a stationary stochastic process is nonergodic when a random persistent topic can be detected in the infinite random text sampled from the process, whereas we call the process strongly nonergodic when an infinite sequence of…
This work deals with a system of interacting reinforced stochastic processes, where each process $X^j=(X_{n,j})_n$ is located at a vertex $j$ of a finite weighted direct graph, and it can be interpreted as the sequence of "actions" adopted…
We establish new conditions for obtaining uniform bounds on the moments of discrete-time stochastic processes. Our results require a weak negative drift criterion along with a state-dependent restriction on the sizes of the one-step jumps…