This paper develops asymptotic properties of singularly perturbed Markov chains with inclusion of absorbing states.It focuses on both unscaled and scaled occupation measures.Under mild conditions,a mean-square estimat...This paper develops asymptotic properties of singularly perturbed Markov chains with inclusion of absorbing states.It focuses on both unscaled and scaled occupation measures.Under mild conditions,a mean-square estimate is obtained.By averaging the fast components,we obtain an aggregated process.Although the aggregated process itself may be non-Markovian,its weak limit is a Markov chain with much smaller state space.Moreover,a suitably scaled sequence consisting of a component of scaled occupation measures and a component of the aggregated process is shown to converge to a pair of processes with a switching diffusion component.展开更多
We investigate a simple evolutionary game model in one dimension. It is found that the system exhibits a discontinuous phase transition from a defection state to a cooperation state when the b payoff of a defector exp...We investigate a simple evolutionary game model in one dimension. It is found that the system exhibits a discontinuous phase transition from a defection state to a cooperation state when the b payoff of a defector exploiting a cooperator is small. Furthermore, if b is large enough, then the system exhibits two continuous phase transitions between two absorbing states and a coexistence state of cooperation and defection, respectively. The tri-critical point is roughly estimated. Moreover, it is found that the critical behavior of the continuous phase transition with an absorbing state is in the directed percolation universality class.展开更多
文摘This paper develops asymptotic properties of singularly perturbed Markov chains with inclusion of absorbing states.It focuses on both unscaled and scaled occupation measures.Under mild conditions,a mean-square estimate is obtained.By averaging the fast components,we obtain an aggregated process.Although the aggregated process itself may be non-Markovian,its weak limit is a Markov chain with much smaller state space.Moreover,a suitably scaled sequence consisting of a component of scaled occupation measures and a component of the aggregated process is shown to converge to a pair of processes with a switching diffusion component.
基金Project supported by the National Natural Science Foundation of China (Grand No. 10575055)K. C. Wong Magna Fund in Ningbo University
文摘We investigate a simple evolutionary game model in one dimension. It is found that the system exhibits a discontinuous phase transition from a defection state to a cooperation state when the b payoff of a defector exploiting a cooperator is small. Furthermore, if b is large enough, then the system exhibits two continuous phase transitions between two absorbing states and a coexistence state of cooperation and defection, respectively. The tri-critical point is roughly estimated. Moreover, it is found that the critical behavior of the continuous phase transition with an absorbing state is in the directed percolation universality class.
