Related papers: Maximum likelihood estimator consistency for balli…

We establish a strong law of large numbers for one-dimensional continuous-time random walks in dynamic random environments under two main assumptions: the environment is required to satisfy a decoupling inequality that can be interpreted as…

The conditions under which entanglement becomes maximal are sought in the general one--dimensional quantum random walk with two walkers. Moreover, a one--dimensional shift operator for the two walkers is introduced and its performance in…

This paper proposes a formal approach to online learning and planning for agents operating in a priori unknown, time-varying environments. The proposed method computes the maximally likely model of the environment, given the observations…

The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so…

The $\lambda$-exponential family generalizes the standard exponential family via a generalized convex duality motivated by optimal transport. It is the constant-curvature analogue of the exponential family from the information-geometric…

We consider random i.i.d. samples of absolutely continuous measures on bounded connected domains. We prove an upper bound on the $\infty$-transportation distance between the measure and the empirical measure of the sample. The bound is…

In this work, we consider the problem of online (real-time, single-shot) estimation of static or slow-varying parameters along quantum trajectories in quantum dynamical systems. Based on the measurement signal of a continuously-monitored…

We define two minimum distance estimators for dependent data by minimizing some approximated Maximum Mean Discrepancy distances between the true empirical distribution of observations and their assumed (parametric) model distribution. When…

We consider a discrete time random walk in one dimension. At each time step the walker jumps by a random distance, independent from step to step, drawn from an arbitrary symmetric density function. We show that the expected positive maximum…

Place an obstacle with probability $1-p$ independently at each vertex of $\mathbb Z^d$, and run a simple random walk until hitting one of the obstacles. For $d\geq 2$ and $p$ strictly above the critical threshold for site percolation, we…

We propose and study properties of maximum likelihood estimators in the class of conditional transformation models. Based on a suitable explicit parameterisation of the unconditional or conditional transformation function, we establish a…

A transient stochastic process is considered strongly transient if conditioned on returning to the starting location, the expected time it takes to return the the starting location is finite. We characterize strong transience for a…

We consider maximum likelihood estimation of finite mixture of uniform distributions. We prove that maximum likelihood estimator is strongly consistent, if the scale parameters of the component uniform distributions are restricted from…

In this article we discuss estimation of the common variance of several normal populations with tree order restricted means. We discuss the asymptotic properties of the maximum likelihood estimator of the variance as the number of…

Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…

Motivated by the random Lorentz gas, we study deterministic walks in random environment and show that (in simple, yet relevant, cases) they can be reduced to a class of random walks in random environment where the jump probability depends…

In this article, we merge celebrated results of Kesten and Spitzer [Z. Wahrsch. Verw. Gebiete 50 (1979) 5-25] and Kawazu and Kesten [J. Stat. Phys. 37 (1984) 561-575]. A random walk performs a motion in an i.i.d. environment and observes an…

We examine a class of random walks in random environments on $\mathbb{Z}$ with bounded jumps, a generalization of the classic one-dimensional model. The environments we study have i.i.d. transition probability vectors drawn from Dirichlet…

We consider the classical estimation problem of an unknown drift parameter within classes of nondegenerate diffusion processes. Using rough path theory (in the sense of T. Lyons), we analyze the Maximum Likelihood Estimator (MLE) with…

Determinantal point processes (DPPs) have wide-ranging applications in machine learning, where they are used to enforce the notion of diversity in subset selection problems. Many estimators have been proposed, but surprisingly the basic…