Related papers: Directed Continuous-Time Random Walk with memory
In this issue we demonstrate the very inspiring role of the continuous-time random walk (CTRW) formalism and its numerous modifications thanks to their flexibility and various applications as well its promising perspectives in different…
The continuous time random walk (CTRW) model exhibits a non-ergodic phase when the average waiting time diverges. Using an analytical approach for the non-biased and the uniformly biased CTRWs, and numerical simulations for the CTRW in a…
This paper reveals that we can interpret the fundamental function of Randomized Time Warping (RTW) as a type of self-attention mechanism, a core technology of Transformers in motion recognition. The self-attention is a mechanism that…
Quantum walks (QWs) exhibit different properties compared with classical random walks (RWs), most notably by linear spreading and localization. In the meantime, random walks that replicate quantum walks, which we refer to as…
We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly-decaying…
In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model,…
In this paper, we introduce the elephant random walk (ERW) with memory consisting of randomly selected steps from its history. It is a time-changed variant of the standard elephant random walk with memory consisting of its full history. At…
Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits…
Continuous time random walks (CTRWs) are versatile models for anomalous diffusion processes that have found widespread application in the quantitative sciences. Their scaling limits are typically non-Markovian, and the computation of their…
The Continuous Time Random Walk (CTRW) formalism is used to model the non-Poisson relaxation of a system response to perturbation. Two mechanisms to perturb the system are analyzed: a first in which the perturbation, seen as a potential…
We study a one-dimensional random walk with memory. The behavior of the walker is modified with respect to the simple symmetric random walk (SSRW) only when he is at the maximum distance ever reached from his starting point (home). In this…
Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy…
We show the asymptotic long-time equivalence of a generic power law waiting time distribution to the Mittag-Leffler waiting time distribution, characteristic for a time fractional CTRW. This asymptotic equivalence is effected by a…
We study memory based random walk models to understand diffusive motion in crowded heterogeneous environment. The models considered are non-Markovian as the current move of the random walk models is determined by randomly selecting a move…
We study analytically, in one dimension, the survival probability $P_{s}(t)$ up to time $t$ of an immobile target surrounded by mutually noninteracting traps each performing a continuous-time random walk (CTRW) in continuous space. We…
Initially developed in the framework of quantum stochastic calculus, the main equations of quantum stochastic filtering were later on derived as the limits of Markov models of discrete measurements under appropriate scaling. In many…
Random walks are a fundamental tool for analyzing realistic complex networked systems and implementing randomized algorithms to solve diverse problems such as searching and sampling. For many real applications, their actual effect and…
We apply the Continuous Time Random Walk (CTRW) framework, introduced in finance by Scalas et al., to the analysis of the probability distribution of time intervals between two consecutive trades in the case of BTP futures prices traded at…
The continuous time random walks (CTRWs) are typically defned in the way that their trajectories are discontinuous step fuctions. This may be a unwellcome feature from the point of view of application of theese processes to model certain…
In this minireview we present the main results regarding the transport properties of stochastic movement with relocations to known positions. To do so, we formulate the problem in a general manner to see several cases extensively studied…