By adopting a nice auxiliary transform of Markov operators, we derive new bounds for the first eigenvalue of the generator corresponding to symmetric Markov processes. Our results not only extend the related topic in ...By adopting a nice auxiliary transform of Markov operators, we derive new bounds for the first eigenvalue of the generator corresponding to symmetric Markov processes. Our results not only extend the related topic in the literature, but also are efficiently used to study the first eigenvalue of birth-death processes with killing and that of elliptic operators with killing on half line. In particular, we obtain two approximation procedures for the first eigenvalue of birth-death processes with killing, and present qualitatively sharp upper and lower bounds for the first eigenvalue of elliptic operators with killing on half line.展开更多
A birth-death process is considered as an epidemic model with recovery and transmittance from outside.The fraction of infected individuals is for huge population sizes approximated by a solution of an ordinary differe...A birth-death process is considered as an epidemic model with recovery and transmittance from outside.The fraction of infected individuals is for huge population sizes approximated by a solution of an ordinary differential equation taking values in[0,1].For intermediate size or semilarge populations,the fraction of infected individuals is approximated by a diffusion formulated as a stochastic differential equation.That diffusion approximation however needs to be killed at the boundary{0}U{1}.An alternative stochastic differential equation model is investigated which instead allows a more natural reflection at the boundary.展开更多
基金Supported by Foundation of Fujian’s Ministry of Education (Grant Nos. JA10058 and JA11051)National Natural Science Foundation of China (Grant No. 11126350)
文摘By adopting a nice auxiliary transform of Markov operators, we derive new bounds for the first eigenvalue of the generator corresponding to symmetric Markov processes. Our results not only extend the related topic in the literature, but also are efficiently used to study the first eigenvalue of birth-death processes with killing and that of elliptic operators with killing on half line. In particular, we obtain two approximation procedures for the first eigenvalue of birth-death processes with killing, and present qualitatively sharp upper and lower bounds for the first eigenvalue of elliptic operators with killing on half line.
文摘A birth-death process is considered as an epidemic model with recovery and transmittance from outside.The fraction of infected individuals is for huge population sizes approximated by a solution of an ordinary differential equation taking values in[0,1].For intermediate size or semilarge populations,the fraction of infected individuals is approximated by a diffusion formulated as a stochastic differential equation.That diffusion approximation however needs to be killed at the boundary{0}U{1}.An alternative stochastic differential equation model is investigated which instead allows a more natural reflection at the boundary.
