Výsledky vyhledávání

Report

Sample path central limit theorem for the occupation time of the voter model on a lattice

Autor: Xue, Xiaofeng

In this paper, we extend the central limit theorem of the occupation time of the voter model on the lattice $\mathbb{Z}^d$ given in \cite{Cox1983} to the sample path case for $d\geq 3$. The proof of our main result utilizes the resolvent strategy and

Externí odkaz: http://arxiv.org/abs/2412.05064

Zobrazit plný text záznamu

Report

Sample path properties and small ball probabilities for stochastic fractional diffusion equations

Autor: Guo, Yuhui, Song, Jian, Wang, Ran, Xiao, Yimin

We consider the following stochastic space-time fractional diffusion equation with vanishing initial condition:$$ \partial^{\beta} u(t, x)=- \left(-\Delta\right)^{\alpha / 2} u(t, x)+ I_{0+}^{\gamma}\left[\dot{W}(t, x)\right],\quad t\in[0,T],\: x \in

Externí odkaz: http://arxiv.org/abs/2411.12192

Zobrazit plný text záznamu

Report

Sample Path Properties of the Fractional Wiener--Weierstrass Bridge

Autor: Schied, Alexander, Zhang, Zhenyuan

Fractional Wiener--Weierstrass bridges are a class of Gaussian processes that arise from replacing the trigonometric function in the construction of classical Weierstrass functions by a fractional Brownian bridge. We investigate the sample path prope

Externí odkaz: http://arxiv.org/abs/2411.05204

Zobrazit plný text záznamu

Report

Sample-Path Large Deviations for L\'evy Processes and Random Walks with Lognormal Increments

Autor: Su, Zhe, Rhee, Chang-Han

The large deviations theory for heavy-tailed processes has seen significant advances in the recent past. In particular, Rhee et al. (2019) and Bazhba et al. (2020) established large deviation asymptotics at the sample-path level for L\'evy processes

Externí odkaz: http://arxiv.org/abs/2410.20799

Zobrazit plný text záznamu

Report

Sample path properties of parabolic SPDEs with non constant coefficients

Autor: Dalang, Robert C., Sanz-Solé, Marta

We consider an SPDE driven by a parabolic second order partial differential operator with a nonlinear random external forcing defined by a Gaussian noise that is white in time and has a spatially homogeneous covariance. We prove existence and uniquen

Externí odkaz: http://arxiv.org/abs/2410.23995

Zobrazit plný text záznamu

Report

Embedding generalization within the learning dynamics: An approach based-on sample path large deviation theory

Autor: Befekadu, Getachew K.

We consider a typical learning problem of point estimations for modeling of nonlinear functions or dynamical systems in which generalization, i.e., verifying a given learned model, can be embedded as an integral part of the learning process or dynami

Externí odkaz: http://arxiv.org/abs/2408.02167

Zobrazit plný text záznamu

Report

Local times of self-intersection and sample path properties of Volterra Gaussian processes

Autor: Izyumtseva, Olga, KhudaBukhsh, Wasiur R.

We study a Volterra Gaussian process of the form $X(t)=\int^t_0K(t,s)d{W(s)},$ where $W$ is a Wiener process and $K$ is a continuous kernel. In dimension one, we prove a law of the iterated logarithm, discuss the existence of local times and verify a

Externí odkaz: http://arxiv.org/abs/2409.04377

Zobrazit plný text záznamu