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Among various mathematical frameworks, multidimensional continuous-time Markov jump processes $(Z_t)$ on $\N^d$ form a natural set-up for modeling $SIR$-like epidemics. In this study we extend the res...
We consider the problem of approximation of the solution of the backward stochastic differential equation in the Markovian case. We suppose that the trend coefficient of the diffusion process depends ...
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary dis...
In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regul...
We study sparse approximation by greedy algorithms. We prove the Lebesgue-type inequalities for the Weak Chebyshev Greedy Algorithm (WCGA), a generalization of the Weak Orthogonal Matching Pursuit to ...
We consider the discrete three dimensional scan statistics. Viewed as the maximum of an 1-dependent stationary r.v.'s sequence, we provide approximations and error bounds for the probability distribut...
Bayesian Reinforcement Learning (RL) is capable of not only incorporating domain knowledge, but also solving the exploration-exploitation dilemma in a natural way. As Bayesian RL is intractable except...
The accuracy of compound Poisson approximation to the sum $S=w_1S_1+w_2S_2+...+w_NS_N$ is estimated. Here $S_i$ are sums of independent or weakly dependent random variables, and $w_i$ denote weights...
It is shown the almost sure convergence and asymptotical normality of a generalization of Kesten's stochastic approximation algorithm for multidimensional case. In this generalization, the step incr...
In this work, we deal with approximations for distribution functions of non-negative random variables. More specifically, we construct continuous approximants using an acceleration technique over a w...
This is a survery paper on Poisson approximation using Stein's method of exchangeable pairs. We illustrate using Poisson-binomial trials and many variations on three classical problems of combinatoria...
In this paper we prove a strong approximation result for a mixing sequence with infinite variance and logarithmic decay rate of the mixing coefficient. The result is proved under the assumption that t...

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