Related papers: Optimal sequential change-detection for fractional…
We study the problem of parameter estimation for the homogenization limit of multiscale systems involving fractional dynamics. In the case of stochastic multiscale systems driven by Brownian motion, it has been shown that in order for the…
The aim of online monitoring is to issue an alarm as soon as there is significant evidence in the collected observations to suggest that the underlying data generating mechanism has changed. This work is concerned with open-end,…
We consider the problem of the Bayesian inference of drift and diffusion coefficient functions in a stochastic differential equation given discrete observations of a realisation of its solution. We give conditions for the well-posedness and…
Detecting if and when objects change is difficult in passive sub-diffraction imaging of dynamic scenes. We consider the best possible tradeoff between responsivity and accuracy for detecting a change from one arbitrary object model to…
In the problem of quickest change detection (QCD), a change occurs at some unknown time in the distribution of a sequence of independent observations. This work studies a QCD problem where the change is either a bad change, which we aim to…
The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics…
We address the problem of quickest change detection in Markov processes with unknown transition kernels. The key idea is to learn the conditional score $\nabla_{\mathbf{y}} \log p(\mathbf{y}|\mathbf{x})$ directly from sample pairs $(…
The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. It is assumed that the pre-change distribution is known (accurately estimated), while the only information about the…
The problem of sequentially finding an independent and identically distributed (i.i.d.) sequence that is drawn from a probability distribution $F_1$ by searching over multiple sequences, some of which are drawn from $F_1$ and the others of…
In this paper, we consider the problem of estimating the drift parameter of solution to the stochastic differential equation driven by a fractional Brownian motion with Hurst parameter less than $1/2$ under complete observation. We derive a…
Single-file diffusion behaves as normal diffusion at small time and as anomalous subdiffusion at large time. These properties can be described by fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We…
We combine the rough path theory and stochastic backward error analysis to develop a new framework for error analysis on numerical schemes. Based on our approach, we prove that the almost sure convergence rate of the modified Milstein…
We propose a general framework of sequential testing procedures based on $U$-statistics which contains as an example a sequential CUSUM test based on differences in mean but also includes a robust sequential Wilcoxon change point procedure.…
We present a distribution-free CUSUM procedure designed for online change detection in a time series of low-rank images, particularly when the change causes a mean shift. We represent images as matrix data and allow for temporal dependence,…
A class of Gaussian processes generalizing the usual fractional Brownian motion for Hurst indices in (1/2,1) and multifractal Brownian motion introduced in Ralchenko and Shevchenko (Theory Probab Math Stat 80, 2010) and Boufoussi et al.…
This article is devoted to study stochastic lattice dynamical systems driven by a fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. First of all, we investigate the existence and uniqueness of pathwise mild solutions to such…
This paper deals with the Local Asymptotical normality for the joint drift parameter and Hurst parameter $H>3/4$ in the mixed fractional Ornstein-Uhlenbeck process. Different from the only estimation of the drift parameter when $H$ is…
An important assumption in the work on testing for structural breaks in time series consists in the fact that the model is formulated such that the stochastic process under the null hypothesis of "no change-point" is stationary. This…
We study well-posedness of sweeping processes with stochastic perturbations generated by a fractional Brownian motion and convergence of associated numerical schemes. To this end, we first prove new existence, uniqueness and approximation…
We address the computational challenge of finding the robust sequential change-point detection procedures when the pre- and post-change distributions are not completely specified. Earlier works [veeravalli 1994] and [Unnikrishnan 2011]…