In this paper, we investigate super-uniformly elliptic diffusions {Xt,t ≥ 0} with its branching mechanism given by ψ(z) = γz1+β(0 < ≤ 1), and, when the initial value X0(dx) is one kind of invariant measures of...In this paper, we investigate super-uniformly elliptic diffusions {Xt,t ≥ 0} with its branching mechanism given by ψ(z) = γz1+β(0 < ≤ 1), and, when the initial value X0(dx) is one kind of invariant measures of the underlying processes, we show that if dimension d satisfies βd ≤ 2, then the random measures Xt will converge to the null in distribution and if βd > 2, then Xt will converge to a nondegenerative random measure in the same sense.展开更多
Some complete variational formulas and approximation theorems for the first eigenvalue of elliptic operators in dimension one or a class of Markov chains are presented.
文摘In this paper, we investigate super-uniformly elliptic diffusions {Xt,t ≥ 0} with its branching mechanism given by ψ(z) = γz1+β(0 < ≤ 1), and, when the initial value X0(dx) is one kind of invariant measures of the underlying processes, we show that if dimension d satisfies βd ≤ 2, then the random measures Xt will converge to the null in distribution and if βd > 2, then Xt will converge to a nondegenerative random measure in the same sense.
基金This work was supported in part bythe National Natural Science Foundation of China (Grant No. 19631060) Mathematical Tian Yuan Foundation, Qiu Shi Science & Technology Foundation, RFDP and MCEC.
文摘Some complete variational formulas and approximation theorems for the first eigenvalue of elliptic operators in dimension one or a class of Markov chains are presented.
