共查询到19条相似文献,搜索用时 140 毫秒
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一类时间随机环境中随机游动 总被引:1,自引:0,他引:1
胡学平 《高校应用数学学报(A辑)》2011,26(1):27-32
利用概率母函数方法,通过对一类时间随机环境中随机游动首中时性质的研究,得到了该随机游动的常返准则和一个强大数定律. 相似文献
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直线上随机环境中可逗留的随机游动的若干性质 总被引:1,自引:0,他引:1
主要研究直线上随机环境中可逗留的随机游动的常返性与极限性质,在独立随机环境下,通过强大数定律给出了常返与暂留的一个充分条件;在一般随机环境下,通过数列的有界性给出了常返与零常返的充分条件并讨论了在独立随机环境下非常返性中的大数定律,从而推广了Solomon的研究框架. 相似文献
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张美娟 《数学年刊B辑(英文版)》2013,34(6):727-736
假定环境平稳遍历, 考虑随机环境中的分枝随机游动. 在此模型中, 粒子以上临界的Galton-Watson 过程分枝产生后代, 而以一维紧邻随机环境中的随机游动进行运动. 令~$Z_{n}(B)$ 表示时间~$n$ 落于~$B$ 中的粒子数, 其中~$B$ 为~$\mathbb{R}$ 中任一子集. 得到了计数测度~$Z_{n}(\cdot)$ 经过适当的规范化之后, 在~``annealed" 情形下的中心极限定理. 相似文献
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讨论了-般环境中二重随机游动的强泛函大数定律,给出了当过程几乎处处趋向于正无穷时的泛函大数定律成立的几个充分条件. 相似文献
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在随机环境中分枝随机游动模型中,粒子的繁衍机制是随机环境中分枝过程,各代粒子在直线上的位置由依赖随机环境的点过程给定,讨论了各代点过程的Laplace变换由其条件期望规范化后的极限性质. 相似文献
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时间随机环境下随机游动的渐近行为 总被引:2,自引:0,他引:2
本文给出了可数状态空间中时间随机环境下随机游动的一个统一的模型 .对于最常见的情况 ,即d维最近邻域随机环境下随机游动 ,如果环境是严平稳的 ,则在一定条件下 ,该随机游动满足强大数定律和中心极限定理 .特别地 ,当环境独立同分布时 ,我们可以得到更为具体的结果 ,该结果类似于经典的随机游动的相应结论 . 相似文献
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半直线上随机环境中的随机游动的常返性 总被引:3,自引:0,他引:3
本文讨论半直线上随机环境中的随机游动的常返性。在独立环境下,主要通过强大数定律,找到了非常返和正常返的一个充分条件下,并将这一结果推广到一些特殊情情形。在一般的随机环境下,主要通过数列的有界性,给出了常返与零常返的一个充分条件。 相似文献
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高志强 《数学物理学报(A辑)》2022,(1):282-305
考虑了Zd中随机环境中的分枝随机游动,其中分枝机制和粒子迁移的分布律均依时间变化.对任意给定点z∈Zd,令Zn(z)表示位于该点处的n代粒子的个数.给出了Zn(z)的二阶渐近展开表达式. 相似文献
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Hua-Ming Wang 《Journal of Theoretical Probability》2018,31(2):619-642
We study a random walk with unbounded jumps in random environment. The environment is stationary and ergodic, uniformly elliptic and decays polynomially with speed \(Dj^{-(3+\varepsilon _0)}\) for some \(D>0\) and small \(\varepsilon _0>0.\) We prove a law of large numbers under the condition that the annealed mean of the hitting time of the lattice of the positive half line is finite. As the second part, we consider a birth and death process with bounded jumps in stationary and ergodic environment whose skeleton process is a random walk with unbounded jumps in random environment. Under a uniform ellipticity condition, we prove a law of large numbers and give the explicit formula of its velocity. 相似文献
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We study a birth and death process $\{N_t\}_{t\ge0}$ in i.i.d. random environment, for which at each discontinuity, one particle might be born or at most $L$ particles might be dead. Along with investigating the existence and the recurrence criterion, we also study the law of large numbers of $\{N_t\}$. We show
that the first passage time can be written as a functional of an $L$-type branching process in random environment and a sequence of independent and exponentially distributed random variables. Consequently, an explicit velocity of the law of large numbers can be given. 相似文献
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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 light-tailed behavior of the stationary distribution is proved under appropriate conditions. The key idea of the method employed here is the decomposition of the trajectory of the random walk and the main tool is the intrinsic branching structure buried in the random walk on a strip, which is different from the matrix-analytic method. 相似文献
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在状态空间是可数情形下,本文给出了时间随机环境下随机游动的一个一般模型.随后,在环境是独立同分布情形下得到了直线上时间随机环境下紧邻随机游动的一个常返与暂留准则和强大数定律;最后讨论了其中心极限定理,它类似与简单随机游动的相应结果. 相似文献
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本文对有向和无向de Bruijn图上的随机游动进行了研究,得出了有向de Bruijn图上简单随机游动任意两点之间平均击中时间的显式表达式,并证明了有向和无向de Bruijn图上随机游动的快速收敛性。 相似文献
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Ekaterina Vladimirovna Bulinskaya 《Journal of Theoretical Probability》2014,27(3):878-898
Critical catalytic branching random walk on an integer lattice ? d is investigated for all d∈?. The branching may occur at the origin only and the start point is arbitrary. The asymptotic behavior, as time grows to infinity, is determined for the mean local particles numbers. The same problem is solved for the probability of the presence of particles at a fixed lattice point. Moreover, the Yaglom type limit theorem is established for the local number of particles. Our analysis involves construction of an auxiliary Bellman–Harris branching process with six types of particles. The proofs employ the asymptotic properties of the (improper) c.d.f. of hitting times with taboo. The latter notion was recently introduced by the author for a non-branching random walk on ? d . 相似文献
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In this article, we mainly discuss the asymptotic behavior for multi-dimensional continuous-time random walk in random environment with holding times. By constructing a renewal structure and using the point "environment viewed from the particle", under General Kalikow's Condition, we show the law of large numbers (LLN) and central limit theorem (CLT) for the escape speed of random walk. 相似文献
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In this paper,we consider the(L,1) state-dependent reflecting random walk(RW) on the half line,which is an RW allowing jumps to the left at a maximal size L.For this model,we provide an explicit criterion for(positive) recurrence and an explicit expression for the stationary distribution.As an application,we prove the geometric tail asymptotic behavior of the stationary distribution under certain conditions.The main tool employed in the paper is the intrinsic branching structure within the(L,1)-random walk. 相似文献