7 papers · 1 filter
Quasihelix properties of selected Volterra Gaussian processes
Yuliya Mishura, Kostiantyn Ralchenko
We study local quasihelix and generalized quasihelix properties of several Gaussian Volterra processes with tempered, power-weighted, and logarithmic kernels, including tempered fr…
Drift parameter estimation in the double mixed fractional Brownian model via solutions of Fredholm equations with singular kernels
Yuliya Mishura, Kostiantyn Ralchenko, Mykyta Yakovliev
We consider drift parameter estimation in a model driven by the sum of two independent fractional Brownian motions with different Hurst indices. Although the maximum likelihood est…
Parameter estimation of integrated fractional Brownian motion
Marco Mastrogiovanni, Yuliya Mishura, Stefania Ottaviano +2
Fractional Brownian motion (fBm) is a canonical model for long-memory phenomena. In the presence of large amounts of potentially memory-bearing data, the data are often averaged, w…
Differential Shannon and Rényi entropies revisited
Yuliya Mishura, Kostiantyn Ralchenko
Shannon entropy for discrete distributions is a fundamental and widely used concept, but its continuous analogue, known as differential entropy, lacks essential properties such as…
Entropy of Wiener integrals with respect to fractional Brownian motion
Iryna Bodnarchuk, Yuliya Mishura, Kostiantyn Ralchenko
The paper is devoted to the properties of the entropy of the exponent-Wiener-integral fractional Gaussian process (EWIFG-process), that is a Wiener integral of the exponent with re…
Entropies of the Poisson distribution as functions of intensity: "normal" and "anomalous" behavior
Dmitri Finkelshtein, Anatoliy Malyarenko, Yuliya Mishura +1
The paper extends the analysis of the entropies of the Poisson distribution with parameter . It demonstrates that the Tsallis and Sharma-Mittal entropies exhibit monotonic beha…