arXiv subjects

Yinghui Shi

Publications and source records attributed to Yinghui Shi.

4 recordsLinked to original sources

arXiv2023

Asymptotic behavior for multi-scale SDEs with monotonicity coefficients driven by Lévy processes

In this paper, we study the asymptotic behavior for multi-scale stochastic differential equations driven by Lévy processes. The optimal strong convergence order 1/2 is obtained by studying the regularity estimates for the solution of Poisson equation with polynomial growth coefficients, and the optimal weak convergence order 1 is got by using the technique of Kolmogorov equation. The main contribution is that the obtained results can be applied to a class of multi-scale stochastic differential equations with monotonicity coefficients, as well as the driven processes can be the general Lévy processes, which seems new in the existing literature.

math.PR↗

arXiv2022

Multi-modal Contrastive Representation Learning for Entity Alignment

Multi-modal entity alignment aims to identify equivalent entities between two different multi-modal knowledge graphs, which consist of structural triples and images associated with entities. Most previous works focus on how to utilize and encode information from different modalities, while it is not trivial to leverage multi-modal knowledge in entity alignment because of the modality heterogeneity. In this paper, we propose MCLEA, a Multi-modal Contrastive Learning based Entity Alignment model, to obtain effective joint representations for multi-modal entity alignment. Different from previous works, MCLEA considers task-oriented modality and models the inter-modal relationships for each entity representation. In particular, MCLEA firstly learns multiple individual representations from multiple modalities, and then performs contrastive learning to jointly model intra-modal and inter-modal interactions. Extensive experimental results show that MCLEA outperforms state-of-the-art baselines on public datasets under both supervised and unsupervised settings.

cs.CL↗

arXiv2021

Well-posedness and averaging principle of McKean-Vlasov SPDEs driven by cylindrical $α$-stable process

In this paper, we first study the well-posedness of a class of McKean-Vlasov stochastic partial differential equations driven by cylindrical $α$-stable process, where $α\in(1,2)$. Then by the method of the Khasminskii's time discretization, we prove the averaging principle of a class of multiscale McKean-Vlasov stochastic partial differential equations driven by cylindrical $α$-stable processes. Meanwhile, we obtain a specific strong convergence rate.

math.PR↗

arXiv2016

Gaussian estimates of the density for systems of non-linear stochastic heat equations

In this paper we consider a system of non-linear stochastic heat equations on $\mathbb{R}^d$ driven by a Gaussian noise which is white in time and has a homogeneous spatial covariance. Under some suitable regularity and non degeneracy conditions, the smoothness of the joint density of the solution for this system has been studied by E. Nualart in [11]. The purpose of this paper is further to study the lower and upper bounds of the density. The main tools are the Malliavin calculus and the method developed by Kohatasu-Higa in [6] or E. Nualart and Quer-Sardanyons in [12].

math.PR↗