A Mechanical Model of Brownian Motion with Uniform Motion Area

Journal of Mathematical Sciences

Liang, Song¹ 

关键词: Infinite particle systems;    non-random mechanics;    Markov process;    diffusion;    convergence;    Brownian motion;    uniform motion.;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

Weconsiderasystemofpluralmassiveparticlesinteractingwithanidealgas,evolvedaccordingtonon-randommechanicalprinciples,viainteractionpotentials.Wefirstprovetheweakconvergenceofthe(position,velocity)-processofthemassiveparticlesuntilcertaintime,underacertainscalinglimit,andgivethepreciseexpressionofthelimitingprocess,adiffusionprocess.Inthesecondhalf,weconsideraspecialcasewhichincludesthecaseof``twosametypemassiveparticles''asaconcreteexample,andprovetheconvergenceoftheprocessofthemassiveparticlesuntilanytime.Theprecisedescriptionofthelimitprocess,acombinationofa``diffusionphase''anda``uniformmotionphase'',isalsogiven.

【 授权许可】

Unknown