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Normalized random measures with independent increments represent a large class of Bayesian nonaprametric priors and are widely used in the Bayesian nonparametric framework. In this paper, we provide the posterior consistency analysis for…
In this paper, we study the asymptotic behavior of a semi-linear slow-fast stochastic partial differential equation with singular coefficients. Using the Poisson equation in Hilbert space, we first establish the strong convergence in the…
In this paper, we present the asymptotic distribution of M-estimators for parameters in non-stationary AR(p) processes. The innovations are assumed to be in the domain of attraction of a stable law with index $0<\alpha\le2$. In particular,…
A key feature of a sequential study is that the actual sample size is a random variable that typically depends on the outcomes collected. While hypothesis testing theory for sequential designs is well established, parameter and precision…
We extend a general result showing that the asymptotic behavior of high moments, factorial or standard, of random variables, determines the asymptotically normality, from the one dimensional to the multidimensional setting. This approach…
We consider discrete-time observations of a continuous martingale under measurement error. This serves as a fundamental model for high-frequency data in finance, where an efficient price process is observed under microstructure noise. It is…
This paper provides a detailed description for the asymptotics of exponential functionals of random walks with light/heavy tails. We give the convergence rate based on the key observation that the asymptotics depends on the sample paths…
We consider the process $\{x-N(t):t\geq 0\}$, where $x\in\mathbb{R}_+$ and $\{N(t):t\geq 0\}$ is a renewal process with light-tailed distributed holding times. We are interested in the joint distribution of $(\tau(x),A(x))$ where $\tau(x)$…
The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. We here discuss a renewal process…
Consider a branching Markov process, $X = (X(t), t \ge 0)$, with non-local branching mechanism. Studying the asymptotic behaviour of the moments of X has recently received attention in the literature [6, 7] due to the importance of these…
We consider Ewens random permutations of length $n$ conditioned to have no cycle longer than $n^\beta$ with $0<\beta<1$ and to study the asymptotic behaviour as $n\to\infty$. We obtain very precise information on the joint distribution of…
In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…
We establish asymptotic properties of $M$-estimators, defined in terms of a contrast function and observations from a continuous-time locally stationary process. Using the stationary approximation of the sequence, $\theta$-weak dependence,…
The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…
Recent fluorescence spectroscopy measurements of single-enzyme kinetics have shown that enzymatic turnovers form a renewal stochastic process in which the inverse of the mean waiting time between turnovers follows the Michaelis-Menten…
We identify general conditions under which regenerative processes with dependent cycles and cycle lengths are asymptotically independent. The result is applied to various models. In particular, independent L\'evy processes with dependent…
For complex latent variable models, the likelihood function is not available in closed form. In this context, a popular method to perform parameter estimation is Importance Weighted Variational Inference. It essentially maximizes the…
We study the variance of the number of zeroes of a stationary Gaussian process on a long interval. We give a simple asymptotic description under mild mixing conditions. This allows us to characterise minimal and maximal growth. We show that…
This paper considers the relative frequencies of distinct types of individuals in multitype branching processes. We prove that the frequencies are asymptotically multivariate normal when the initial number of ancestors is large and the time…
In this paper, a novel non-parametric method for estimation of expectation and maximum value of the variance function is proposed for recurrent events where intensity of event occurrence changes with the occurrence of each higher order…