Related papers: Asymptotics of weighted random sums

For the renormalised sums of the random $\pm 1$-colouring of the connected components of $\mathbb Z$ generated by the coalescing renewal processes in the "power law P\'olya's urn" of Hammond and Sheffield we prove functional convergence…

The familiar cascade measures are sequences of random positive measures obtained on $[0,1]$ via $b$-adic independent cascades. To generalize them, this paper allows the random weights invoked in the cascades to take real or complex values.…

This paper investigates $\pi_T(a_1,a_2) = \mathbb{P}\left(\sup\limits_{t\in[0,T]} (\sigma_1B(t)-c_1t)>a_1, \sup\limits_{t\in[0,T]}( \sigma_2 B(t)-c_2t)>a_2\right),$ where $\{B(t) : t \geq 0\}$ is a standard Brownian motion, with $T >0,…

We will study the asymptotic behavior of summation functions of a natural argument, including the asymptotic behavior of summation functions of a prime argument in the paper. A general formula is obtained for determining the asymptotic…

Given a Brownian Motion $W$, in this paper we study the asymptotic behavior, as $\eps \to 0$, of the quadratic covariation between $f (\eps W)$ and $W$ in the case in which $f$ is not smooth. Among the main features discovered is that the…

In this paper we obtain a rate of convergence in the central limit theorem for high order weighted Hermite variations of the fractional Brownian motion. The proof is based on the techniques of Malliavin calculus and the quantitative stable…

In this paper, a class of statistics based on high frequency observations of oscillating and skew Brownian motion is considered. Their convergence rate towards the local time of the underlying process is obtained in form of a functional…

We prove an invariance principle for Brownian motion in Gaussian or Poissonian random scenery by the method of characteristic functions. Annealed asymptotic limits are derived in all dimensions, with a focus on the case of dimension $d=2$,…

Motivated by applications in functional data analysis, we study the partial sum process of sparsely observed, random functions. A key novelty of our analysis are bounds for the distributional distance between the limit Brownian motion and…

The invariance properties of Brownian motion are investigated and revisited within a recent Lie symmetry approach to stochastic differential equations. Some notable properties of the process can be recovered by a related integration by…

We revisit the problem of condensation for independent, identically distributed random variables with a power-law tail, conditioned by the value of their sum. For large values of the sum, and for a large number of summands, a condensation…

We study the asymptotic behavior of estimators of a two-valued, discontinuous diffusion coefficient in a Stochastic Differential Equation, called an Oscillating Brownian Motion. Using the relation of the latter process with the Skew…

We define and prove the existence of a fractional Brownian motion indexed by a collection of closed subsets of a measure space. This process is a generalization of the set-indexed Brownian motion, when the condition of independance is…

The aim of this paper is to investigate discrete approximations of the exponential functional $\int_0^{\infty} \exp(B(t) - \nu t) \di t$ of Brownian motion (which plays an important role in Asian options of financial mathematics) by the…

We prove that the random empirical measure of appropriately rescaled particle trajectories of the interchange process on path graphs converges weakly to the deterministic measure of stationary Brownian motion on the unit interval. This is a…

In this paper we study the asymptotic behavior of the angular bispectrum of spherical random fields. Here, the asymptotic theory is developed in the framework of fixed-radius fields, which are observed with increasing resolution as the…

We propose a simple conjecture for the functional form of the asymptotic behavior of work distributions for driven overdamped Brownian motion of a particle in confining potentials. This conjecture is motivated by the fact that these…

We present a complete characterization of the asymptotic behaviour of a correlated Bernoulli sequence { which depends on the parameter $\theta \in [0,1]$. A martingale theory based approach will allow} us to prove versions of the law of…

We study the asymptotic behaviour of the probability that a weighted sum of centered i.i.d. random variables X_k does not exceed a constant barrier. For regular random walks, the results follow easily from classical fluctuation theory,…

We elaborate on the theorem saying that as permeability coefficients of snapping-out Brownian motions tend to infinity in such a way that their ratio remains constant, these processes converge to a skew Brownian motion. In particular,…