The Fleming-Viot process with parent-independent mutation process is one particular neutral pop- ulation genetic model. As time goes by, some initial species are replaced by mutated ones gradually. Once the population...The Fleming-Viot process with parent-independent mutation process is one particular neutral pop- ulation genetic model. As time goes by, some initial species are replaced by mutated ones gradually. Once the population mutation rate is high, mutated species will elbow out all the initial species very quickly. Small-time behavior in thls case seems to be the key to understand this fast transition. The small-time asymptotic results related to time scale t and a（O）t, where lim0→∞θ θa（θ） = O, are obtained by Dawson and Shni （1998, 2001）, Shui and Xiong （2002）, and Xiang and Zhang （2005）, respectively. Only the behavior under the scale t（θ）, where limθ→∞θt（θ） = 0 and limθ→∞（O） =∞ was left untouched. In this paper, the weak limits under various small-time scales are obtained. Of particular interest is the large deviations for the small-time transient sam- pling distributions, which reveal interesting phase transition. Interestingly, such a phase transition is uniquely determined by some species diversity indices.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
This is a survey on the strong uniqueness of the solutions to stochastic partial differential equations(SPDEs) related to two measure-valued processes: superprocess and Fleming-Viot process which are given as rescalin...This is a survey on the strong uniqueness of the solutions to stochastic partial differential equations(SPDEs) related to two measure-valued processes: superprocess and Fleming-Viot process which are given as rescaling limits of population biology models. We summarize recent results for Konno-Shiga-Reimers’ and Mytnik’s SPDEs, and their related distribution-function-valued SPDEs.展开更多
We illustrate a metric geometry viewpoint for large deviation principles by analyzing the proof of a long-standing conjecture on an explicit Schilder-type theorem for super-Brownian motions given by the authors recent...We illustrate a metric geometry viewpoint for large deviation principles by analyzing the proof of a long-standing conjecture on an explicit Schilder-type theorem for super-Brownian motions given by the authors recently,and by understanding sample path large deviations for Fleming-Viot processes.展开更多
基金supported by Fundamental Research Fund of Zhongnan University of Economics and Law (Grant No. 31541411208)
文摘The Fleming-Viot process with parent-independent mutation process is one particular neutral pop- ulation genetic model. As time goes by, some initial species are replaced by mutated ones gradually. Once the population mutation rate is high, mutated species will elbow out all the initial species very quickly. Small-time behavior in thls case seems to be the key to understand this fast transition. The small-time asymptotic results related to time scale t and a（O）t, where lim0→∞θ θa（θ） = O, are obtained by Dawson and Shni （1998, 2001）, Shui and Xiong （2002）, and Xiang and Zhang （2005）, respectively. Only the behavior under the scale t（θ）, where limθ→∞θt（θ） = 0 and limθ→∞（O） =∞ was left untouched. In this paper, the weak limits under various small-time scales are obtained. Of particular interest is the large deviations for the small-time transient sam- pling distributions, which reveal interesting phase transition. Interestingly, such a phase transition is uniquely determined by some species diversity indices.
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.
基金Supported partially by SUST startup fund 28/Y01286120NSF of Ningxia(2018AAC03245)+1 种基金NSFC(11771018)First-Class Disciplines Foundation Ningxia(NXYLXK2017B09)
文摘This is a survey on the strong uniqueness of the solutions to stochastic partial differential equations(SPDEs) related to two measure-valued processes: superprocess and Fleming-Viot process which are given as rescaling limits of population biology models. We summarize recent results for Konno-Shiga-Reimers’ and Mytnik’s SPDEs, and their related distribution-function-valued SPDEs.
基金supported by National Natural Science Foundation of China(Grant Nos.10971106 and 11271204)
文摘We illustrate a metric geometry viewpoint for large deviation principles by analyzing the proof of a long-standing conjecture on an explicit Schilder-type theorem for super-Brownian motions given by the authors recently,and by understanding sample path large deviations for Fleming-Viot processes.
