Related papers: Optimal estimation of some random quantities of a …
In many random search processes of interest in chemistry, biology or during rescue operations, an entity must find a specific target site before the latter becomes inactive, no longer available for reaction or lost. We present exact results…
This paper studies a stochastic mean-field linear-quadratic optimal control problem with random coefficients. The state equation is a general linear stochastic differential equation with mean-field terms $\EE X(t)$ and $\EE u(t)$ of the…
We show that exact sampling of the first passage event can be done for a Levy process with unbounded variation, if the process can be embedded in a subordinated standard Brownian motion. By sampling a series of first exit events of the…
In this paper, we present a statistical framework for modeling conditional quantiles of spatial processes assumed to be strongly mixing in space. We establish the $L_1$ consistency and the asymptotic normality of the kernel conditional…
In this paper, we focus on multiple sampling problems for the estimation of the fractional Brownian motion when the maximum number of samples is limited, extending existing results in the literature in a non-Markovian framework. Two classes…
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…
In this paper, we use quantization to construct a nonparametric estimator of conditional quantiles of a scalar response $Y$ given a d-dimensional vector of covariates $X$. First we focus on the population level and show how optimal…
Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate optimality and efficiency are of…
Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…
This paper studies an optimization-based state estimation approach for discrete-time nonlinear systems under bounded process and measurement disturbances. We first introduce a full information estimator (FIE), which is given as a solution…
We study the efficiency of random search processes based on L{\'e}vy flights with power-law distributed jump lengths in the presence of an external drift, for instance, an underwater current, an airflow, or simply the bias of the searcher…
We construct in the small-time setting the upper and lower estimates for the transition probability density of a L\'evy process in $\rn$. Our approach relies on the complex analysis technique and the asymptotic analysis of the inverse…
We study the asymptotic normality of two feasible estimators of the integrated volatility of volatility based on the Fourier methodology, which does not require the pre-estimation of the spot volatility. We show that the bias-corrected…
This article studies the finite sample behaviour of a number of estimators for the integrated power volatility process of a Brownian semistationary process in the non semi-martingale setting. We establish three consistent feasible…
Let $B = (B_t)_{t \in {\bf R}}$ be a symmetric Brownian motion, i.e. $(B_t)_{t \in {\bf R}_+}$ and $(B_{-t})_{t \in {\bf R}_+}$ are independent Brownian motions starting at $0$. Given $a \ge b>0$, we describe the law of the random set…
In this paper, we study some aspects on random analysis on the L\'eevy stochastic processes with margins following generalized hyperbolic distributions generated by gamma laws. In particular we study the boundedness of its total variations…
We propose an optimization formulation for the simultaneous estimation of a latent variable and the identification of a linear continuous-time dynamic system, given a single input-output pair. We justify this approach based on Bayesian…
In the present paper we consider the varying coefficient model which represents a useful tool for exploring dynamic patterns in many applications. Existing methods typically provide asymptotic evaluation of precision of estimation…
The Blumenthal-Getoor (BG) index characterizes the jump measure of an infinitely active L\'evy process. It determines sample path properties and affects the behavior of various econometric procedures. If the process contains a diffusion…
We consider the problem of designing experiments for the estimation of a target in regression analysis if there is uncertainty about the parametric form of the regression function. A new optimality criterion is proposed, which minimizes the…