arXiv subjects

Svitlana Kushnirenko

Publications and source records attributed to Svitlana Kushnirenko.

3 recordsLinked to original sources

arXiv2024

Driven by Brownian motion Cox-Ingersoll-Ross and squared Bessel processes: interaction and phase transition

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 properties, focusing on time-asymptotic growth rates, distance between the processes in integral norms, and parameter estimation. The squared Bessel process is shown to be a phase transition of the CIR process and can be approximated by a sequence of CIR processes. Differences in stochastic stability are also highlighted, with the Bessel process displaying instability, while the CIR process remains ergodic and stable.

math.PR↗

arXiv2017

Asymptotic behavior of functionals of the solutions to inhomogeneous Itô stochastic differential equations with nonregular dependence on parameter

The asymptotic behavior, as $T\to\infty$, of some functionals of the form $I_T(t)=F_T(ξ_T(t))+\int_0^tg_T(ξ_T(s))\,dW_T(s)$, $t\ge0$ is studied. Here $ξ_T(t)$ is the solution to the time-inhomogeneous Itô stochastic differential equation \[dξ_T(t)=a_T\bigl(t,ξ_T(t)\bigr)\,dt+dW_T(t),\quad t\ge0, ξ_T(0)=x_0,\] $T>0$ is a parameter, $a_T(t,x),x\in\mathbb{R}$ are measurable functions, $|a_T(t,x)|\leq C_T$ for all $x\in\mathbb{R}$ and $t\ge0$, $W_T(t)$ are standard Wiener processes, $F_T(x),x\in\mathbb{R}$ are continuous functions, $g_T(x),x\in\mathbb{R}$ are measurable locally bounded functions, and everything is real-valued. The explicit form of the limiting processes for $I_T(t)$ is established under nonregular dependence of $a_T(t,x)$ and $g_T(x)$ on the parameter $T$.

math.PR↗

arXiv2016

Asymptotic behavior of homogeneous additive functionals of the solutions of Itô stochastic differential equations with nonregular dependence on parameter

We study the asymptotic behavior of mixed functionals of the form $I_T(t)=F_T(ξ_T(t))+\int_0^tg_T(ξ_T(s))\,dξ_T(s)$, $t\ge0$, as $T\to\infty$. Here $ξ_T(t)$ is a strong solution of the stochastic differential equation $dξ_T(t)=a_T(ξ_T(t))\,dt+dW_T(t)$, $T>0$ is a parameter, $a_T=a_T(x)$ are measurable functions such that $\left|a_T(x)\right|\leq C_T$ for all $x\in \mathbb {R}$, $W_T(t)$ are standard Wiener processes, $F_T=F_T(x)$, $x\in \mathbb {R}$, are continuous functions, $g_T=g_T(x)$, $x\in \mathbb {R}$, are locally bounded functions, and everything is real-valued. The explicit form of the limiting processes for $I_T(t)$ is established under very nonregular dependence of $g_T$ and $a_T$ on the parameter $T$.

math.PR↗