Related papers: A central limit theorem for the sample autocorrela…
We obtain necessary and sufficient conditions for the regular variation of the variance of partial sums of functionals of discrete and continuous-time stationary Markov processes with normal transition operators. We also construct a class…
We develop at-the-money call-price and implied volatility asymptotic expansions in time to maturity for a class of asset-price models whose log returns follow a L\'evy process. Under mild assumptions placing the driving L\'evy process in…
This article introduces the class of continuous time locally stationary wavelet processes. Continuous time models enable us to properly provide scale-based time series models for irregularly-spaced observations for the first time, while…
L\'evy-type walks with correlated jumps, induced by the topology of the medium, are studied on a class of one-dimensional deterministic graphs built from generalized Cantor and Smith-Volterra-Cantor sets. The particle performs a standard…
This work focuses on the temporal average of the backward Euler--Maruyama (BEM) method, which is used to approximate the ergodic limit of stochastic ordinary differential equations with super-linearly growing drift coefficients. We give the…
The investigation asymptotic limits on associated data mainly focused on limit theorems of summands of associated data and on the related invariance principles. In a series of papers, we are going to set the general frame of the theory by…
In this article, we introduce a system of stochastic differential equations (SDEs) consisting of time-dependent covariates and consider both fixed and random effects set-ups. We also allow the functional part associated with the drift…
This article treats long term average impulse control problems with running costs in the case that the underlying process is a L\'evy process. Under quite general conditions we characterize the value of the control problem as the value of a…
Ordered pivotal sampling is one of the simplest algorithm to perform without-replacement unequal probability sampling. It has found uses in the context of longitudinal surveys and spatial sampling, and enables in particular a good spatial…
A continuous-time nonlinear regression model with L\'evy-driven linear noise process is considered. Sufficient conditions of consistency and asymptotic normality of the Whittle estimator for the parameter of the noise spectral density are…
A classical limit theorem of stochastic process theory concerns the sample cumulative distribution function (CDF) from independent random variables. If the variables are uniformly distributed then these centered CDFs converge in a suitable…
We consider asymptotic behavior of Fourier transforms of stationary ergodic sequences with finite second moments. We establish a central limit theorem (CLT) for almost all frequencies and also an annealed CLT. The theorems hold for all…
We study the asymptotics of large, moderate and normal deviations for the connected components of the sparse random graph by the method of stochastic processes. We obtain the logarithmic asymptotics of large deviations of the joint…
Donsker-type functional limit theorems are proved for empirical processes arising from discretely sampled increments of a univariate L\'evy process. In the asymptotic regime the sampling frequencies increase to infinity and the limiting…
In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal…
In this paper, we study the asymptotic behavior of a fully-coupled slow-fast McKean-Vlasov stochastic system. Using the non-linear Poisson equation on Wasserstein space, we first establish the strong convergence in the averaging principle…
We consider simple random walk on a realization of an Erd\H{o}s-R\'enyi graph that is asymptotically almost surely (a.a.s.) connected. We show a Central Limit Theorem (CLT) for the average starting hitting time, i.e. the expected time it…
Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a $d$-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are…
A variety of estimators for the parameters of the Generalized Pareto distribution, the approximating distribution for excesses over a high threshold, have been proposed, always assuming the underlying data to be independent. We recently…
Linear structural error-in-variables models with univariate observations are revisited for studying modified least squares estimators of the slope and intercept. New marginal central limit theorems (CLT's) are established for these…