Filipp Buryak | Searcharxiv

arXiv2021

Convexity and robustness of the Rényi entropy

We study convexity properties of Rényi entropy as function of $α>0$ on finite alphabets. We also describe robustness of the Rényi entropy on finite alphabets, and it turns out that the rate of respective convergence depends on initial alphabet. We establish convergence of the disturbed entropy when the initial distribution is uniform but the number of events increases to $\infty$ and prove that limit of Rényi entropy of binomial distribution is equal to Rényi entropy of Poisson distribution.

math.PR↗

arXiv2020

Distance from fractional Brownian motion with associated Hurst index $0<H<1/2$ to the subspaces of Gaussian martingales involving power integrands with an arbitrary positive exponent

We find the best approximation of the fractional Brownian motion with the Hurst index $H\in (0,1/2)$ by Gaussian martingales of the form $\int _0^ts^γdW_s$, where $W$ is a Wiener process, $γ>0$.

math.PR↗