The Dirichlet distribution that we are concerned with in this paper is very special, in which all parameters are different from each other. We prove that the asymptotic distribution of this kind of Dirichlet distribut...The Dirichlet distribution that we are concerned with in this paper is very special, in which all parameters are different from each other. We prove that the asymptotic distribution of this kind of Dirichlet distributions is a normal distribution by using the central limit theorem and Slutsky theorem.展开更多
For any N≥2 andα=(α1…,αN+1)∈(0,∞)^N+1,letμa^(N)be the Dirichlet distribution with parameterαon the set△(N):={x^μa∈[0,1]^N:∑1≤i≤N^xi≤1}.The multivariate Dirichlct diffusion is associated with the Dirich...For any N≥2 andα=(α1…,αN+1)∈(0,∞)^N+1,letμa^(N)be the Dirichlet distribution with parameterαon the set△(N):={x^μa∈[0,1]^N:∑1≤i≤N^xi≤1}.The multivariate Dirichlct diffusion is associated with the Dirichlet formεa^(N)(f,f):=∑n=i^N∫△(N)(1-∑1≤i≤N^xi)xn(Эnf)^2(x)μα^(N)(dx)with Domain D(εa^(N))being the closure of C^1(△^(N)).We prove the Nash inequalityμa^(N)(f^2)≤Cεa^(N)(f,f)^p/(p+1)μa^(N)(|f|)^2/(p+1),f∈D(εa^(N)),μa^(N)(f)=0 for some constant C>0 and p=(aN+1-1)++∑i^N=11∨(2ai),where the constant p is sharp when max1≤i≤N ai≤1/2 and aN+1≥1.This Nash inequality also holds for the corresponding Fleming-Viot process.展开更多
基金Plan Project of Department of Education Science and Technology of Jilin Province,No.152[2007]
文摘The Dirichlet distribution that we are concerned with in this paper is very special, in which all parameters are different from each other. We prove that the asymptotic distribution of this kind of Dirichlet distributions is a normal distribution by using the central limit theorem and Slutsky theorem.
基金The authors would like to thank the referees for helpful comments on an earlier version of the paper.This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11771326,11726627,11831014).
文摘For any N≥2 andα=(α1…,αN+1)∈(0,∞)^N+1,letμa^(N)be the Dirichlet distribution with parameterαon the set△(N):={x^μa∈[0,1]^N:∑1≤i≤N^xi≤1}.The multivariate Dirichlct diffusion is associated with the Dirichlet formεa^(N)(f,f):=∑n=i^N∫△(N)(1-∑1≤i≤N^xi)xn(Эnf)^2(x)μα^(N)(dx)with Domain D(εa^(N))being the closure of C^1(△^(N)).We prove the Nash inequalityμa^(N)(f^2)≤Cεa^(N)(f,f)^p/(p+1)μa^(N)(|f|)^2/(p+1),f∈D(εa^(N)),μa^(N)(f)=0 for some constant C>0 and p=(aN+1-1)++∑i^N=11∨(2ai),where the constant p is sharp when max1≤i≤N ai≤1/2 and aN+1≥1.This Nash inequality also holds for the corresponding Fleming-Viot process.
