Transport by Molecular Motors in the Presence of Static Defects

The transport by molecular motors along cytoskeletal filaments is studied theoretically in the presence of static defects. The movements of single motors are described as biased random walks along the filament as well as binding to and unbinding from the filament. Three basic types of defects are distinguished, which differ from normal filament sites only in one of the motors’ transition probabilities. Both stepping defects with a reduced probability for forward steps and unbinding defects with an increased probability for motor unbinding strongly reduce the velocities and the run lengths of the motors with increasing defect density. For transport by single motors, binding defects with a reduced probability for motor binding have a relatively small effect on the transport properties. For cargo transport by motors teams, binding defects also change the effective unbinding rate of the cargo particles and are expected to have a stronger effect.     

一维紧邻时间随机环境下可逗留随机游动的有关性质

给出了可数状态空间中时间随机环境下可逗留随机游动的一个统一模型,对于一维紧邻时间随机环境下的随机游动,在一定的条件下,讨论它的极限性质和中心极限定理,该结论类似于空间随机环境下的随机游动的有关结论.     

关于随机环境中的马尔可夫过程的简介——纪念李国平院士吴新谋教授诞辰100周年

该文系统地介绍随机环境中的马尔可夫过程. 共4章, 第一章介绍依时的随机环境中的马尔可夫链(MCTRE), 包括MCTRE的存在性及等价描述; 状态分类; 遍历理论及不变测度; p-θ 链的中心极限定理和不变原理. 第二章介绍依时的随机环境中的马尔可夫过程(MPTRE), 包括MPTRE的基本概念; 随机环境中的q -过程存在唯一性; 时齐的q -过程;MPTRE的构造及等价性定理.第三章介绍依时的随机环境中的分枝链(MBCRE), 包括有限维的和无穷维的MBCRE的模型和基本概念; 它们的灭绝概念;两极分化; 增殖率等.第四章介绍依时依空的随机环境中的马尔可夫链(MCSTRE), 包括MCSTRE的基本概念、构造; 依时依空的随机环境中的随机徘徊(RWSTRE)的中心极限定理、不变原理.     

Weak convergence to Rosenblatt sheet

We study the problem of the approximation in law of the Rosenblatt sheet. We prove the convergence in law of two families of process to the Rosenblatt sheet: the first one is constructed from a Poisson process in the plane and the second one is based on random walks.     

CTRW模型等待时间分布的随机抽样方法

研究等待时间分布为截断幂律分布的连续时间随机行走(CTRW)模型,分析比较截断幂律分布的可能随机抽样方法,并提出一套可以对其进行精确抽样的乘分布舍选算法.数值结果表明:当幂律指数α > 0.2时,该算法的抽样效率在80%以上.利用该算法可以成功得出CTRW模型描述的三种反常输运过程的标度关系.     

Invariance principle for biased bootstrap random walks

Our main goal is to study a class of processes whose increments are generated via a cellular automata rule. Given the increments of a simple biased random walk, a new sequence of (dependent) Bernoulli random variables is produced. It is built, from the original sequence, according to a cellular automata rule. Equipped with these two sequences, we construct two more according to the same cellular automata rule. The construction is repeated a fixed number of times yielding an infinite array ($\{?K,\dots ,K\}\times \mathbb{N}$) of (dependent) Bernoulli random variables. Taking partial sums of these sequences, we obtain a $(2K+1)$-dimensional process whose increments belong to the state space ${\{?1,1\}}^{2K+1}$.The aim of the paper is to study the long term behaviour of this process. In particular, we establish transience/recurrence properties and prove an invariance principle. The limiting behaviour of these processes depends strongly on the direction of the iteration, and exhibits few surprising features. This work is motivated by an earlier investigation (see Collevecchio et al. (2015)), in which the starting sequence is symmetric, and by the related work Ferrari et al. (2000).     

Selective Limit Theorems for Random Walks on Parabolic Biangle and Triangle Hypergroups

Let K be respectively the parabolic biangle and the triangle in and be a sequence in [0, +[ such that lim_p (p)=+. According to Koornwinder and Schwartz,⁽⁷⁾ for each there exist a convolution structure (*_(p)) such that (K, *_(p)) is a commutative hypergroup. Consider now a random walk on (K, *_(p)), assume that this random walk is stopped after j(p) steps. Then under certain conditions given below we prove that the random variables on K admit a selective limit theorems. The proofs depend on limit relations between the characters of these hypergroups and Laguerre polynomials that we give in this work.     

一类分形结构上的非对称随机游动

本研究一类分形结构上的随机游动,得到了它的进位不变性,进位时间的生成函数表达式并得到一个极限定理。     

Finitely additive random walks on infinitely generated free groups

We consider any purely finitely additive probability measure supported on the generators of an infinitely generated free group and the Markov strategy with stationary transition probability . As well as for the case of random walks (with countably additive transition probability) on finitely generated free groups, we prove that all bounded sets are transient. Finally, we consider any finitely additive measure (supported on the group generators) and we prove that the classification of the state space depends only on the continuous part of .