RANDOM_WALK

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Extremum of a time-inhomogeneous branching random walk
《Frontiers of Mathematics in China》2021年第2期459-478,共20页Wanting HOU Xiaoyue ZHANG Wenming HONG 
This work was supported by the National Key Research and Development Program of China(No.2020YFA0712900);the National Natural Science Foundation of China(Grant NO.11971062);the Fundamental Research Funds for the Central Universities Grant(No.N180503019).
Consider a time-inhomogeneous branching random walk, generated by the point process Ln which composed by two independent parts: ‘branching’offspring Xn with the mean 1+B(1+n)−β for β∈(0,1) and ‘displacement’ ξ...
关键词：Branching random walk time-inhomogeneous branching process random walk 
Scaling limit theorem for transient random walk in random environment
《Frontiers of Mathematics in China》2018年第5期1033-1044,共12页Wenming HONG Hui YANG 
We construct a sequence of transient random walks in random environments and prove that by proper scaling, it converges to a diffusion process with drifted Brownian potential. To this end, we prove a counterpart of co...
关键词：Random walk random environment diffusion process Brownian motion with drift 
Scaling limit of local time of Sinai＇s random walk
《Frontiers of Mathematics in China》2015年第6期1313-1324,共12页Wenming HONG Hui YANG Ke ZHOU 
Acknowledgements The authors thank the anonymous referees for their very careful reading of the manuscript. This work was supported in part by the National Natural Science Foundation of China （Grant No. 10721091） and the 985-project.
We prove that the local times of a sequence of Sinai＇s random walks converge to those of Brox＇s diffusion by proper scaling. Our proof is based on the intrinsic branching structure of the random walk and the converg...
关键词：Sinai＇s random walk random environment local time Brox＇s diffusion branching process 
Laws of iterated logarithm for transient random walks in random environments
《Frontiers of Mathematics in China》2015年第4期857-874,共18页Fuqing GAO 
The author would like to thank the referees for comments on conditions （C1） and （C2）. This work was supported in part by the National Natural Science Foundation of China （Grant No. 11171262） and the Specialized Research Fund for the Doctoral Program of Higher Education of China （Grant No. 20130141110076）.
We consider laws of iterated random walks in random environments. logarithm for one-dimensional transient A quenched law of iterated logarithm is presented for transient random walks in general ergodic random environm...
关键词：Laws of iterated logarithm random walk random environment 
Light-tailed behavior of stationary distribution for state-dependent random walks on a strip被引量：2
《Frontiers of Mathematics in China》2014年第4期813-834,共22页Wenming HONG Meijuan ZHANG Yiqiang Q. ZHAO 
Acknowledgements The authors would like to thank Drs. Hongyan Sun and Ke Zhou for their stimulating discussion. Also they would like to express their gratitude to the referees for their careful reading of the first version of paper and useful suggestions for revising the paper. This work was partially supported by the National Natural Science Foundation of China （Grant No. 11131003）, the 985 Project, and the Natural Sciences and Engineering Research Council of Canada （Grant No. 315660）.
We consider the state-dependent reflecting random walk on a half- strip. We provide explicit criteria for （positive） recurrence, and an explicit expression for the stationary distribution. As a consequence, the ligh...
关键词：Random walk on a strip stationary distribution light-tailedbehavior branching process RECURRENCE state-dependent 
Tail behavior of supremum of a random walk when Cramer＇s condition fails
《Frontiers of Mathematics in China》2014年第2期431-453,共23页Changjun YU Yuebao WANG 
Acknowledgements The authors were grateful to the two reviewers for their valuable comments and suggestions to improve the present paper. This work was supported by the National Natural Science Foundation of China （NO. 11071182） and the Doctor Introduction Foundation of Nantong University （No. 12R066）.
We investigate tail behavior of the supremum of a random walk in the case that Cramer＇s condition fails, namely, the intermediate case and the heavy-tailed ease. When the integrated distribution of the increment of t...
关键词：Random walk SUPREMUM exponential distribution class O-subexponential distribution class closure property asymptotic estimate ruin probability 
Voter model in a random environment in Zd被引量：1
《Frontiers of Mathematics in China》2012年第5期895-905,共11页Zhichao SHAN Dayue CHEN 
We consider the voter model with flip rates determined by {ue, e ∈ Ed}, where Ed is the set of all non-oriented nearest-neighbour edges in the Euclidean lattice Zd. Suppose that {ue, e ∈ Ed} are independent and iden...
关键词：Voter model random walk random environment DUALITY 
Mean and variance of first passage time of non-homogeneous random walk被引量：2
《Frontiers of Mathematics in China》2012年第3期551-559,共9页Huaming WANG 
The prime concern of this paper is the first passage time of a nonhomogeneous random walk, which is nearest neighbor but able to stay at its position. It is revealed that the branching structure of the walk correspond...
关键词：Random walk 2-type branching process first passage time variance 
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