An L2-approximation method for construction and smoothing estimates of Markov semigroups for interacting diffusion processes on a lattice

Won Yong Sul

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An L2-approximation method for construction and smoothing estimates of Markov semigroups for interacting diffusion processes on a lattice

机译：LATOV半群施工和平滑估计的L2近似方法，用于在晶格中相互作用的扩散过程

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摘要

We develop an L2-approximation strategy to study Markov semigroups generated by an infinite system of elliptic diffusion processes on a lattice. The proposed dynamics incorporate nearest neighbor interactions influencing diffusivity, which has received little attention so far as a mathematical problem. We prove the existence and the smoothness of Markov semigroups by extending the well-known pointwise estimation techniques such as the finite speed of propagation property and the Lyapunov function methods.

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《Infinite dimensional analysis, quantum probability, and related topics》 |2021年第1期|共21页
作者
Won Yong Sul;
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作者单位

Natl Inst Math Sci Div Med Math Daejeon 34047 South Korea;

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原文格式 PDF
正文语种 eng
中图分类物理学;
关键词
Markov semigroup; interacting particle systems; finite speed of propagation; infinite dimensions; smoothing estimates; collective diffusion;

机译：马尔可夫半群;交互粒子系统;传播有限速度;无限尺寸;平滑估计;集体扩散;

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5. Nonlinear Markov Semigroups and Interacting Lévy Type Processes [J] . Vassili N. Kolokoltsov Journal of Statistical Physics . 2007,第3期

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7. UNIFORM IN TIME ESTIMATES FOR THE WEAK ERROR OF THE EULER METHOD FOR SDES AND A PATHWISE APPROACH TO DERIVATIVE ESTIMATES FOR DIFFUSION SEMIGROUPS [J] . Crisan D., Dobson P., Ottobre M. Transactions of the American Mathematical Society . 2021,第5期

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8. An Anisotropic Diffusion Model for Medical Image Smoothing by Using the Lattice Boltzmann Method [C] . Yu Chen, Zhuangzhi Yan, YueHong Qian 7th Asian-Pacific Conference on Medical and Biological Engineering（第七届亚太地区生物工程学术会议）论文集 . 2008

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9. Error estimates for stabilized approximation methods for semigroups [D] . McAllister, Sarah Campbell 2005

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11. Nonlinear Markov Semigroups and Interacting Lévy Type Processes [O] . Vassili N. Kolokoltsov 2010

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An L2-approximation method for construction and smoothing estimates of Markov semigroups for interacting diffusion processes on a lattice

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