Related papers: On the mean projection theorem for determinantal p…

By using a multiscale analysis, we establish quantitative versions of the Besicovitch projection theorem (almost every projection of a purely unrectifiable set in the plane of finite length has measure zero) and a standard companion result,…

Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…

We consider prediction theory for stationary stochastic processes in continuous time. We discuss prediction using the whole (infinite) past, and using only a finite section of the past. The solutions to both these classical problems have…

In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are…

Determinantal processes on half-integer line can be studied using vertex algebras. They were used by Okounkov, where Schur processes were introduced and proved to be determinantal. We want to extend this vertex algebra approach. First, we…

We prove a law of large numbers in terms of complete convergence of independent random variables taking values in increments of monotone functions, with convergence uniform both in the initial and the final time. The result holds also for…

We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…

The classical arithmetic Grothendieck-Riemann-Roch theorem can be applied only to projective morphisms that are smooth over the complex numbers. In this paper we generalize the arithmetic Grothendieck-Riemann-Roch theorem to the case of…

In this work, we develop variational formulations of Petrov-Galerkin type for one-dimensional fractional boundary value problems involving either a Riemann-Liouville or Caputo derivative of order $\alpha\in(3/2, 2)$ in the leading term and…

In this paper, a class of piecewise deterministic Markov processes with underlying fast dynamic is studied. Using a "penalty method" , an averaging result is obtained when the underlying dynamic is infinitely accelerated. The features of…

In the case of finite measures on finite spaces, we state conditions under which {\phi}- projections are continuously differentiable. When the set on which one wishes to {\phi}- project is convex, we show that the required assumptions are…

We address the challenge of correlated predictors in high-dimensional GLMs, where regression coefficients range from sparse to dense, by proposing a data-driven random projection method. This is particularly relevant for applications where…

The paper presents sufficient conditions of predictability for continuous time processes in deterministic setting. We found that processes with exponential decay on energy for higher frequencies are predictable in some weak sense on some…

We present a general black box theorem that ensures convergence of a sequence of stationary Markov processes, provided a few assumptions are satisfied. This theorem relies on a control of the resolvents of the sequence of Markov processes,…

In this work we introduce new approximate similarity relations that are shown to be key for policy (or control) synthesis over general Markov decision processes. The models of interest are discrete-time Markov decision processes, endowed…

We extend the options framework for temporal abstraction in reinforcement learning from discounted Markov decision processes (MDPs) to average-reward MDPs. Our contributions include general convergent off-policy inter-option learning…

In this paper, we will derive the first and 2nd order Wiener chaos decomposition for the multivariate linear statistics of the determinantal point processes associated with the spectral projection kernels on the unit spheres $S^d$. We will…

We explore the interplay between random and deterministic phenomena using a representation of uncertainty based on the measure-theoretic concept of outer measure. The meaning of the analogues of different probabilistic concepts is…

We obtain asymptotic formulae for the second discrete moments of the Riemann zeta function over arithmetic progressions $\frac{1}{2} + i(a n + b)$. It reveals noticeable relation between the discrete moments and the continuous moment of the…

The argmax theorem is a useful result for deriving the limiting distribution of estimators in many applications. The conclusion of the argmax theorem states that the argmax of a sequence of stochastic processes converges in distribution to…