Related papers: Stable Central Limit Theorems for Super Ornstein-U…

Let $(X_{k})_{k \in \mathbb Z }$ be a linear process with values in a separable Hilbert space $\mathbb{H}$ given by $X_{k} =\sum_{j=0}^{\infty} (j+1)^{-N}\varepsilon_{k-j}$ for each $k \in \mathbb Z$, where $N:\mathbb{H} \to \mathbb{H}$ is…

For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the…

We show that deliberately breaking detailed balance in generative diffusion processes can accelerate the reverse process without changing the stationary distribution. Considering the Ornstein--Uhlenbeck process, we decompose the dynamics…

Assuming that a threshold Ornstein-Uhlenbeck process is observed at discrete time instants, we propose generalized moment estimators to estimate the parameters. Our theoretical basis is the celebrated ergodic theorem. To use this theorem we…

In this article we prove new results regarding the existence of Bernstein processes associated with the Cauchy problem of certain forward-backward systems of decoupled linear deterministic parabolic equations defined in Euclidean space of…

We establish an almost sure scaling limit theorem for super-Brownian motion on $\mathbb{R}^d$ associated with the semi-linear equation $u_t = {1/2}\Delta u +\beta u-\alpha u^2$, where $\alpha$ and $\beta$ are positive constants. In this…

This paper presents the asymptotic theory for nondegenerate $U$-statistics of high frequency observations of continuous It\^{o} semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem…

In this paper we introduce the well-balanced L\'{e}vy driven Ornstein-Uhlenbeck process as a moving average process of the form $X_t=\int \exp(-\lambda |t-u|)dL_u$. In contrast to L\'{e}vy driven Ornstein-Uhlenbeck processes the…

We use asymptotic methods from the theory of differential equations to obtain an analytical expression for the survival probability of an Ornstein-Uhlenbeck process with a potential defined over a broad domain. We form a uniformly…

We consider the branching process in random environment $\{Z_n\}_{n\geq 0}$, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We focus…

Our goal is to establish large deviations and concentration inequalities for the maximum likelihood estimator of the drift parameter of the Ornstein-Uhlenbeck process without tears. We propose a new strategy to establish large deviation…

We investigate nonequilibrium critical properties of $O(n)$-symmetric models with reversible mode-coupling terms. Specifically, a variant of the model of Sasv\'ari, Schwabl, and Sz\'epfalusy is studied, where violation of detailed balance…

Let $X$ be a $n$-dimensional Ornstein-Uhlenbeck process, solution of the S.D.E. $$\d X_t = AX_t \d t + \d B_t$$ where $A$ is a real $n\times n$ matrix and $B$ a L\'evy process without Gaussian part. We show that when $A$ is non-singular,…

The relaxation of a dissipative system to its equilibrium state often shows a multiexponential pattern with relaxation rates, which are typically considered to be independent of the initial condition. The rates follow from the spectrum of a…

This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of…

In this article, we prove the analogue theorems of Stein-Tomas and Srtichartz on the discrete surface restrictions of Fourier-Hermite transforms associated with the normalized Hermite polynomials and obtain the Strichartz estimate for the…

Let $Z:=\{Z_t,t\geq0\}$ be a stationary Gaussian process. We study two estimators of $\mathbb{E}[Z_0^2]$, namely $\widehat{f}_T(Z):= \frac{1}{T} \int_{0}^{T} Z_{t}^{2}dt$, and $\widetilde{f}_n(Z) :=\frac{1}{n} \sum_{i =1}^{n}…

Based on discrete observations $X_0,X_{\Delta},\dots, X_{n\Delta}$ for $\Delta=n^{-\gamma}$ with $\gamma\in [0,1)$ of the null-recurrent dynamic $dX_t = \sigma(X_t)dW_t$ with a Brownian motion $W$ and $\sigma(x)=\alpha\mathbb{1}\{x<\rho\} +…

We investigate the dynamical stability and phase transition behavior in a holographic superfluid model incorporating higher-order self-interaction terms $\lambda |\psi|^4$, $\tau|\psi|^6$, and a non-minimal coupling…

We consider a supercritical branching process $Z_n$ in a stationary and ergodic random environment $\xi =(\xi_n)_{n\ge0}$. Due to the martingale convergence theorem, it is known that the normalized population size $W_n=Z_n/ (\mathbb E…