5 papers · 1 filter
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…
Gatheral double stochastic volatility model with Skorokhod reflection
Yuliya Mishura, Andrey Pilipenko, Kostiantyn Ralchenko
We investigate the Gatheral model of double mean-reverting stochastic volatility, in which the drift term itself follows a mean-reverting process, and the overall model exhibits me…
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…
Functional limit theorems for a time-changed multidimensional Wiener process
Yuliia Mishura, René L. Schilling
We study the asymptotic behaviour of a properly normalized time-changed multidimensional Wiener process; the time change is given by an additive functional of the Wiener process it…