64 citations · 320 across the 79 of their papers we have counts for
15 papers · 1 filter
Sandwiched SDEs with unbounded drift driven by Hölder noises
Giulia Di Nunno, Yuliya Mishura, Anton Yurchenko-Tytarenko
We study a stochastic differential equation with an unbounded drift and general Hölder continuous noise of an arbitrary order. The corresponding equation turns out to have a unique…
Convergence results for the Time-Changed fractional Ornstein-Uhlenbeck processes
Giacomo Ascione, Yuliya Mishura, Enrica Pirozzi
In this paper we study some convergence results concerning the one-dimensional distribution of a time-changed fractional Ornstein-Uhlenbeck process. In particular, we establish tha…
On mild and weak solutions for stochastic heat equations with piecewise-constant conductivity
Yuliya Mishura, Kostiantyn Ralchenko, Mounir Zili
We investigate a stochastic partial differential equation with second order elliptic operator in divergence form, having a piecewise constant diffusion coefficient, and driven by a…
Fractional Ornstein-Uhlenbeck process with stochastic forcing and its applications
Giacomo Ascione, Yuliya Mishura, Enrica Pirozzi
We consider a fractional Ornstein-Uhlenbeck process involving a stochastic forcing term in the drift, as a solution of a linear stochastic differential equation driven by a fractio…
Stochastic differential equations driven by additive Volterra-Lévy and Volterra-Gaussian noises
Giulia Di Nunno, Yuliya Mishura, Kostiantyn Ralchenko
We study the existence and uniqueness of solutions to stochastic differential equations with Volterra processes driven by Lévy noise. For this purpose, we study in detail smoothnes…
Approximate solution of the integral equations involving kernel with additional singularity
Vitalii Makogin, Yuliya Mishura, Hanna Zhelezniak
The paper is devoted to the approximate solutions of the Fredholm integral equations of the second kind with the weak singular kernel that can have additional singularity in the nu…
Distance from fractional Brownian motion with associated Hurst index to the subspaces of Gaussian martingales involving power integrands with an arbitrary positive exponent
Oksana Banna, Filipp Buryak, Yuliya Mishura
We find the best approximation of the fractional Brownian motion with the Hurst index by Gaussian martingales of the form , where is a Wiener p…
Perpetual Integral Functionals of Multidimensional Stochastic Processes
Yuri Kondratiev, Yuliya Mishura, José L. da Silva
The paper is devoted to the existence of integral functionals for several classes of processes in with . Some examples s…
How does tempering affect the local and global properties of fractional Brownian motion?
Ehsan Azmoodeh, Yuliya Mishura, Farzad Sabzikar
The present paper investigates the effects of tempering the power law kernel of moving average representation of a fractional Brownian motion (fBm) on some local and global propert…
Two methods of estimation of the drift parameters of the Cox-Ingersoll-Ross process: continuous observations
Olena Dehtiar, Yuliya Mishura, Kostiantyn Ralchenko
We consider a stochastic differential equation of the form , where , and are positive constants. The solution corresponds to the…
Asymptotic behaviour and functional limit theorems for a time changed Wiener process
Yuri Kondratiev, Yuliya Mishura, René L. Schilling
We study the asymptotic behaviour of a properly normalized time changed Wiener processes. The time change reflects the fact that we consider the Laplace operator (which generates a…
The Fokker-Planck equation for the time-changed fractional Ornstein-Uhlenbeck process
Giacomo Ascione, Yuliya Mishura, Enrica Pirozzi
In this paper we study some properties of the generalized Fokker-Planck equation induced by the time-changed fractional Ornstein-Uhlenbeck process. First of all, we exploit some su…
Fractional integrals, derivatives and integral equations with weighted Takagi-Landsberg functions
Vitalii Makogin, Yuliya Mishura
In this paper we find fractional Riemann-Liouville derivatives for the Takagi-Landsberg functions. Moreover, we introduce their generalizations called weighted Takagi-Landsberg fun…
Fractional Cox--Ingersoll--Ross process with small Hurst indices
Yuliya Mishura, Anton Yurchenko-Tytarenko
In this paper the fractional Cox-Ingersoll-Ross process on for is defined as a square of a pointwise limit of the processes , satisfying the…
Gaussian processes with Volterra kernels
Yuliya Mishura, Georgiy Shevchenko, Sergiy Shklyar
We study Volterra processes , where is a standard Wiener process, and the kernel has the form . This form gen…