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math.PR2021
Standard and fractional reflected Ornstein-Uhlenbeck processes as the limits of square roots of Cox-Ingersoll-Ross processes
Yuliya Mishura, Anton Yurchenko-Tytarenko
In this paper, we establish a new connection between Cox-Ingersoll-Ross (CIR) and reflected Ornstein-Uhlenbeck (ROU) models driven by either a standard Wiener process or a fraction…
math.PR2021
Convexity and robustness of the Rényi entropy
Filipp Buryak, Yuliya Mishura
We study convexity properties of Rényi entropy as function of on finite alphabets. We also describe robustness of the Rényi entropy on finite alphabets, and it turns out that…
math.PR2021
Divergence of an integral of a process with small ball estimate
Yuliya Mishura, Nakahiro Yoshida
The paper contains sufficient conditions on the function and the stochastic process that supply the rate of divergence of the integral functional at th…