64 citations · 320 across the 79 of their papers we have counts for
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Driven by Brownian motion Cox-Ingersoll-Ross and squared Bessel processes: interaction and phase transition
Yuliya Mishura, Kostiantyn Ralchenko, Svitlana Kushnirenko
This paper studies two related stochastic processes driven by Brownian motion: the Cox-Ingersoll-Ross (CIR) process and the Bessel process. We investigate their shared and distinct…
Fractional Gaussian noise: Projections, prediction, norms
Iryna Bodnarchuk, Yuliya Mishura, Kostiantyn Ralchenko
We examine the one-sided and two-sided (bilateral) projections of an element of fractional Gaussian noise onto its neighboring elements. We establish several analytical results and…
Gaussian Volterra processes as models of electricity markets
Yuliya Mishura, Stefania Ottaviano, Tiziano Vargiolu
We introduce a non-Markovian model for electricity markets where the spot price of electricity is driven by several Gaussian Volterra processes, which can be e.g., fractional Brown…
A class of infinite-dimensional Gaussian processes defined through generalized fractional operators
Luisa Beghin, Lorenzo Cristofaro, Yuliya Mishura
The generalization of fractional Brownian motion in infinite-dimensional white and grey noise spaces has been recently carried over, following the Mandelbrot-Van Ness representatio…
Parameter estimation in rough Bessel model
Yuliya Mishura, Anton Yurchenko-Tytarenko
In this paper, we construct consistent statistical estimators of the Hurst index, volatility coefficient, and drift parameter for Bessel processes driven by fractional Brownian mot…
Fractional diffusion Bessel processes with Hurst index
Yuliya Mishura, Kostiantyn Ralchenko
We introduce fractional diffusion Bessel process with Hurst index , derive a stochastic differential equation for it, and study the asymptotic properties of its sa…