Some properties of Super-Brownian motion have been approached by Dawson & Hochberg [1], Iscoe [2] & L3], Konno & Shiga [4] and so on. In this paper, we limit our attention to the occupation time processes ...Some properties of Super-Brownian motion have been approached by Dawson & Hochberg [1], Iscoe [2] & L3], Konno & Shiga [4] and so on. In this paper, we limit our attention to the occupation time processes of the Super-Brownian motion,and try to give an intuitive proof for their absolute continuity with respect to the Lebesgue measure on Rd (d≤3) when the initial measure of the Super-Brownian motion has the absolute continuity.展开更多
Suppose that Xt is the Fleming-Viot process associated with fractional power Laplacian operator -(-△)α/2 0 < α≥ 2, and Yt= f_0￣t Xs.ds is the so-called occupation time process.In this paper) the asymptotic be...Suppose that Xt is the Fleming-Viot process associated with fractional power Laplacian operator -(-△)α/2 0 < α≥ 2, and Yt= f_0￣t Xs.ds is the so-called occupation time process.In this paper) the asymptotic behavior at a large time and the absolute continuity of Yt are investigated.展开更多
A class of superprocesses which dies out is investigated.Under the condition of norextinction, a new superprocess is constructed,its life time is infinite, and its distribution is determined by the moment function. Se...A class of superprocesses which dies out is investigated.Under the condition of norextinction, a new superprocess is constructed,its life time is infinite, and its distribution is determined by the moment function. Several limit theorems about this superprocess and its occupation time process are obtained.展开更多
We prove fluctuation limit theorems for the occupation times of super-Brownian motion with immigration. The weak convergence of the processes is established, which improves the results in references. The limiting proc...We prove fluctuation limit theorems for the occupation times of super-Brownian motion with immigration. The weak convergence of the processes is established, which improves the results in references. The limiting processes are Gaussian processes.展开更多
文摘Some properties of Super-Brownian motion have been approached by Dawson & Hochberg [1], Iscoe [2] & L3], Konno & Shiga [4] and so on. In this paper, we limit our attention to the occupation time processes of the Super-Brownian motion,and try to give an intuitive proof for their absolute continuity with respect to the Lebesgue measure on Rd (d≤3) when the initial measure of the Super-Brownian motion has the absolute continuity.
文摘Suppose that Xt is the Fleming-Viot process associated with fractional power Laplacian operator -(-△)α/2 0 < α≥ 2, and Yt= f_0￣t Xs.ds is the so-called occupation time process.In this paper) the asymptotic behavior at a large time and the absolute continuity of Yt are investigated.
文摘A class of superprocesses which dies out is investigated.Under the condition of norextinction, a new superprocess is constructed,its life time is infinite, and its distribution is determined by the moment function. Several limit theorems about this superprocess and its occupation time process are obtained.
基金supported by National Natural Science Foundation of China (Grant No.10721091)
文摘We prove fluctuation limit theorems for the occupation times of super-Brownian motion with immigration. The weak convergence of the processes is established, which improves the results in references. The limiting processes are Gaussian processes.
