Related papers: How linear reinforcement affects Donsker's Theorem…

The paper deals with the problem of finding the best alternatives on the basis of pairwise comparisons when these comparisons need not be transitive. In this setting, we study a reinforcement urn model. We prove convergence to the optimal…

We consider a discrete-time random walk where the random increment at time step $t$ depends on the full history of the process. We calculate exactly the mean and variance of the position and discuss its dependence on the initial condition…

Let v be a bounded function with bounded support in R^d, d>=3. Let x,y in R^d. Let Z(t) denote the path integral of v along the path of a Brownian bridge in R^d which runs for time t, starting at x and ending at y. As t->infty, it is…

We consider the entropy of sums of independent discrete random variables, in analogy with Shannon's Entropy Power Inequality, where equality holds for normals. In our case, infinite divisibility suggests that equality should hold for…

Let $X,X_1,X_2,\cdots$ be independent real valued random variables with a common distribution function $F$, and consider $\{X_1,\cdots,X_N \}$, possibly a big concrete data set, or an imaginary random sample of size $N\geq 1$ on $X$. In the…

We propose and test a method to interpolate sparsely sampled signals by a stochastic process with a broad range of spatial and/or temporal scales. To this end, we extend the notion of a fractional Brownian bridge, defined as fractional…

In [O'Connell and Yor (2002)] a path-transformation G was introduced with the property that, for X belonging to a certain class of random walks on the integer lattice, the transformed walk G(X) has the same law as that of the original walk…

We develop a continuous-time entropy-regularized reinforcement learning framework under model uncertainty. By applying Sion's minimax theorem, we transform the intractable robust control problem into an equivalent standard…

We propose a path transformation which applied to a cyclically exchangeable increment process conditions its minimum to belong to a given interval. This path transformation is then applied to processes with start and end at zero. It is seen…

We consider an empirical process based upon ratio of selected pair of the non-overlapping $m$-spacings generated by independent samples of arbitrary sizes. As a main result, we show that when both samples are uniformly distributed on…

We consider several critical wetting models. In the discrete case, these probability laws are known to converge, after an appropriate rescaling, to the law of a reflecting Brownian motion, or of the modulus of a Brownian bridge, according…

In this paper, we prove maximal inequalities and study the functional central limit theorem for the partial sums of linear processes generated by dependent innovations. Due to the general weights, these processes can exhibit long-range…

Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In this paper we consider two such likelihood ratios. The first one is an…

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

We introduce a three-parameter random walk with reinforcement, called the $(\theta,\alpha,\beta)$ scheme, which generalizes the linearly edge reinforced random walk to uncountable spaces. The parameter $\beta$ smoothly tunes the…

We prove that in wide generality the critical curve of the activated random walk model is a continuous function of the deactivation rate, and we provide a bound on its slope which is uniform with respect to the choice of the graph.…

We find a sharp combinatorial bound for the metric entropy of sets in R^n and general classes of functions. This solves two basic combinatorial conjectures on the empirical processes. 1. A class of functions satisfies the uniform Central…

The step-reinforced random walk (SRRW), where each step may replicate a randomly chosen past step, exhibits complex dependencies on the history. This paper introduces a generalized SRRW on groups, incorporating arbitrary transformations of…

We study the once-reinforced random walk on $\mathbb Z^d$, which is a self-interacting walk that has a higher probability to cross edges that were already visited. We prove that the walk is transient when $d\ge 6$ and when the reinforcement…

We introduce a new technique to establish Hungarian multivariate theorems. In this article we apply this technique to the strong approximation bivariate theorems of the uniform empirical process. It improves the Komlos, Major and Tusn\'ady…