Related papers: Nonparametric estimation of linear multiplier for …
Consider the fractional Brownian Motion (fBM) $B^H=\{B^H(t): t \in [0,1] \}$ with Hurst index $H\in (0,1)$. We construct a probability space supporting both $B^H$ and a fully simulatable process $\hat B_{\epsilon}^H $ such that $$\sup_{t\in…
Assuming that a stochastic process $X=(X_t)_{t\geq 0}$ is a sum of a compound Poisson process $Y=(Y_t)_{t\geq 0}$ with known intensity $\lambda$ and unknown jump size density $f,$ and an independent Brownian motion $Z=(Z_t)_{t\geq 0},$ we…
We derive the asymptotic behavior of weighted quadratic variations of fractional Brownian motion $B$ with Hurst index $H=1/4$. This completes the only missing case in a very recent work by I. Nourdin, D. Nualart and C. A. Tudor. Moreover,…
Let $B_{H}(t), t\geq [0,T], T\in(0,\infty)$ be the standard Multifractional Brownian Motion(mBm), in this contribution we are concerned with the exact asymptotics of \begin{eqnarray*} \mathbb{P}\left\{\sup_{t\in[0,T]}B_{H}(t)>u\right\}…
We investigate the fractional Hardy-H\'enon equation with fractional Brownian noise $$ \partial_tu(t)+(-\Delta)^{\theta/2} u(t)=|x|^{-\gamma} |u(t)|^{p-1}u(t)+\mu \, \partial_t B^H(t), $$ where $\theta>0$, $p>1$, $\gamma\geq 0$, $\mu…
Stochastic differential equations and stochastic dynamics are good models to describe stochastic phenomena in real world. In this paper, we study N independent stochastic processes Xi(t) with real entries and the processes are determined by…
We study parameter estimation problem for diagonalizable stochastic partial differential equations driven by a multiplicative fractional noise with any Hurst parameter $H\in(0,1)$. Two classes of estimators are investigated: traditional…
The article is devoted to the nonparametric estimation of the quadratic covariation of non-synchronously observed It\^o processes in an additive microstructure noise model. In a high-frequency setting, we aim at establishing an asymptotic…
The paper presents a multiplicative bias reduction estimator for nonparametric regression. The approach consists to apply a multiplicative bias correction to an oversmooth pilot estimator. In Burr et al. [2010], this method has been tested…
We study a process satisfying a one-dimensional stochastic differential equation driven by fractional Brownian motion with Hurst index $H>1/2$, and consider the weighted power variation based on the second order differences of the process.…
The paper is devoted to three-parametric self-similar Gaussian Volterra processes that generalize fractional Brownian motion. We study the asymptotic growth of such processes and the properties of long- and short-range dependence. Then we…
This paper generalizes a part of the theory of $Z$-estimation which has been developed mainly in the context of modern empirical processes to the case of stochastic processes, typically, semimartingales. We present a general theorem to…
The aim of this paper is to prove an analogue of Baxter's inequality for fractional Brownian motion-type processes with Hurst index less than 1/2. This inequality is concerned with the norm estimate of the difference between finite- and…
We study the asymptotic behavior of mixed functionals of the form $I_T(t)=F_T(\xi_T(t))+\int_0^tg_T(\xi_T(s))\,d\xi_T(s)$, $t\ge0$, as $T\to\infty$. Here $\xi_T(t)$ is a strong solution of the stochastic differential equation…
A 2D Stochastic incompressible non-Newtonian fluids driven by fractional Bronwnian motion with Hurst parameter $H \in (1/2,1)$ is studied. The Wiener-type stochastic integrals are introduced for infinite-dimensional fractional Brownian…
We introduce a novel method for estimating the self-similarity index of a general $H$-self-similar process with either stationary or non-stationary increments. The estimation algorithm is developed based on a modified Lamperti…
Strongly consistent and asymptotically normal estimators of the Hurst index and volatility parameters of solutions of stochastic differential equations with polynomial drift are proposed. The estimators are based on discrete observations of…
We study the small ball asymptotics problem in $L_2$ for two generalizations of the fractional Brownian motion with variable Hurst parameter. To this end, we perform careful analysis of the singular values asymptotics for associated…
We study the asymptotic behavior of the least squares estimators of the unknown parameters of bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence…
We deal with a planar random flight $\{(X(t),Y(t)),0<t\leq T\}$ observed at $n+1$ equidistant times $t_i=i\Delta_n,i=0,1,...,n$. The aim of this paper is to estimate the unknown value of the parameter $\lambda$, the underlying rate of the…