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Journal articles on the topic 'Continuous Time Random Walk'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Lin, Fang, and Jing-Dong Bao. "Environment-dependent continuous time random walk." Chinese Physics B 20, no. 4 (2011): 040502. http://dx.doi.org/10.1088/1674-1056/20/4/040502.

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2

Wang, Wanli, Eli Barkai, and Stanislav Burov. "Large Deviations for Continuous Time Random Walks." Entropy 22, no. 6 (2020): 697. http://dx.doi.org/10.3390/e22060697.

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Recently observation of random walks in complex environments like the cell and other glassy systems revealed that the spreading of particles, at its tails, follows a spatial exponential decay instead of the canonical Gaussian. We use the widely applicable continuous time random walk model and obtain the large deviation description of the propagator. Under mild conditions that the microscopic jump lengths distribution is decaying exponentially or faster i.e., Lévy like power law distributed jump lengths are excluded, and that the distribution of the waiting times is analytical for short waiting

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3

Hwang, Kyo-Shin, and Wensheng Wang. "Chover-Type Laws of the Iterated Logarithm for Continuous Time Random Walks." Journal of Applied Mathematics 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/906373.

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A continuous time random walk is a random walk subordinated to a renewal process used in physics to model anomalous diffusion. In this paper, we establish Chover-type laws of the iterated logarithm for continuous time random walks with jumps and waiting times in the domains of attraction of stable laws.

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4

Meerschaert, Mark M., and Hans-Peter Scheffler. "Limit theorems for continuous-time random walks with infinite mean waiting times." Journal of Applied Probability 41, no. 3 (2004): 623–38. http://dx.doi.org/10.1239/jap/1091543414.

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A continuous-time random walk is a simple random walk subordinated to a renewal process used in physics to model anomalous diffusion. In this paper we show that, when the time between renewals has infinite mean, the scaling limit is an operator Lévy motion subordinated to the hitting time process of a classical stable subordinator. Density functions for the limit process solve a fractional Cauchy problem, the generalization of a fractional partial differential equation for Hamiltonian chaos. We also establish a functional limit theorem for random walks with jumps in the strict generalized doma

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5

Meerschaert, Mark M., and Hans-Peter Scheffler. "Limit theorems for continuous-time random walks with infinite mean waiting times." Journal of Applied Probability 41, no. 03 (2004): 623–38. http://dx.doi.org/10.1017/s002190020002043x.

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A continuous-time random walk is a simple random walk subordinated to a renewal process used in physics to model anomalous diffusion. In this paper we show that, when the time between renewals has infinite mean, the scaling limit is an operator Lévy motion subordinated to the hitting time process of a classical stable subordinator. Density functions for the limit process solve a fractional Cauchy problem, the generalization of a fractional partial differential equation for Hamiltonian chaos. We also establish a functional limit theorem for random walks with jumps in the strict generalized doma

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6

Alemany, P. A., R. Vogel, I. M. Sokolov, and A. Blumen. "A dumbbell's random walk in continuous time." Journal of Physics A: Mathematical and General 27, no. 23 (1994): 7733–38. http://dx.doi.org/10.1088/0305-4470/27/23/016.

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7

Sabhapandit, Sanjib. "Record statistics of continuous time random walk." EPL (Europhysics Letters) 94, no. 2 (2011): 20003. http://dx.doi.org/10.1209/0295-5075/94/20003.

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8

Becker-Kern, Peter, and Hans-Peter Scheffler. "On multiple-particle continuous-time random walks." Journal of Applied Mathematics 2004, no. 3 (2004): 213–33. http://dx.doi.org/10.1155/s1110757x04308065.

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Scaling limits of continuous-time random walks are used in physics to model anomalous diffusion in which particles spread at a different rate than the classical Brownian motion. In this paper, we characterize the scaling limit of the average of multiple particles, independently moving as a continuous-time random walk. The limit is taken by increasing the number of particles and scaling from microscopic to macroscopic view. We show that the limit is independent of the order of these limiting procedures and can also be taken simultaneously in both procedures. Whereas the scaling limit of a singl

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9

Lv, Longjin, Fu-Yao Ren, Jun Wang, and Jianbin Xiao. "Correlated continuous time random walk with time averaged waiting time." Physica A: Statistical Mechanics and its Applications 422 (March 2015): 101–6. http://dx.doi.org/10.1016/j.physa.2014.12.010.

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10

Zhang, Caiyun, Yuhang Hu, and Jian Liu. "Correlated continuous-time random walk with stochastic resetting." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 9 (2022): 093205. http://dx.doi.org/10.1088/1742-5468/ac8c8e.

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Abstract It is known that the introduction of stochastic resetting in an uncorrelated random walk process can lead to the emergence of a stationary state, i.e. the diffusion evolves towards a saturation state, and a steady Laplace distribution is reached. In this paper, we turn to study the anomalous diffusion of the correlated continuous-time random walk considering stochastic resetting. Results reveal that it displays quite different diffusive behaviors from the uncorrelated one. For the weak correlation case, the stochastic resetting mechanism can slow down the diffusion. However, for the s

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11

Briozzo, Carlos B., Carlos E. Budde, and Manuel O. Cáceres. "Continuous-time random-walk model for superionic conductors." Physical Review A 39, no. 11 (1989): 6010–15. http://dx.doi.org/10.1103/physreva.39.6010.

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12

Denisov, S. I., and H. Kantz. "Continuous-time random walk theory of superslow diffusion." EPL (Europhysics Letters) 92, no. 3 (2010): 30001. http://dx.doi.org/10.1209/0295-5075/92/30001.

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13

Lv, Longjin, Jianbin Xiao, Liangzhong Fan, and Fuyao Ren. "Correlated continuous time random walk and option pricing." Physica A: Statistical Mechanics and its Applications 447 (April 2016): 100–107. http://dx.doi.org/10.1016/j.physa.2015.12.013.

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14

Jiang, Jianguo, and Jichun Wu. "Continuous time random walk in homogeneous porous media." Journal of Contaminant Hydrology 155 (December 2013): 82–86. http://dx.doi.org/10.1016/j.jconhyd.2013.08.006.

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15

Dybiec, Bartłomiej, and Ewa Gudowska-Nowak. "Subordinated diffusion and continuous time random walk asymptotics." Chaos: An Interdisciplinary Journal of Nonlinear Science 20, no. 4 (2010): 043129. http://dx.doi.org/10.1063/1.3522761.

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16

Sokolov, I. M., R. Vogel, P. A. Alemany, and A. Blumen. "Continuous-time random walk of a rigid triangle." Journal of Physics A: Mathematical and General 28, no. 23 (1995): 6645–53. http://dx.doi.org/10.1088/0305-4470/28/23/016.

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17

Hilfer, R., and R. Orbach. "Continuous time random walk approach to dynamic percolation." Chemical Physics 128, no. 1 (1988): 275–87. http://dx.doi.org/10.1016/0301-0104(88)85076-6.

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18

Fa, Kwok Sau, and R. S. Mendes. "A continuous time random walk model with multiple characteristic times." Journal of Statistical Mechanics: Theory and Experiment 2010, no. 04 (2010): P04001. http://dx.doi.org/10.1088/1742-5468/2010/04/p04001.

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19

Chisaki, Kota, Norio Konno, Etsuo Segawa, and Yutaka Shikano. "Crossovers induced by discrete-time quantum walks." Quantum Information and Computation 11, no. 9&10 (2011): 741–60. http://dx.doi.org/10.26421/qic11.9-10-2.

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We consider crossovers with respect to the weak convergence theorems from a discrete-time quantum walk (DTQW). We show that a continuous-time quantum walk (CTQW) and discrete- and continuous-time random walks can be expressed as DTQWs in some limits. At first we generalize our previous study [Phys. Rev. A \textbf{81}, 062129 (2010)] on the DTQW with position measurements. We show that the position measurements per each step with probability $p \sim 1/n^\beta$ can be evaluated, where $n$ is the final time and $0<\beta<1$. We also give a corresponding continuous-time case. As a consequence

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20

Rosenthal, Jeffrey S. "Random walks on discrete and continuous circles." Journal of Applied Probability 30, no. 4 (1993): 780–89. http://dx.doi.org/10.2307/3214512.

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We consider a large class of random walks on the discrete circle Z/(n), defined in terms of a piecewise Lipschitz function, and motivated by the ‘generation gap' process of Diaconis. For such walks, we show that the time until convergence to stationarity is bounded independently of n. Our techniques involve Fourier analysis and a comparison of the random walks on Z/(n) with a random walk on the continuous circle S1.

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21

Rosenthal, Jeffrey S. "Random walks on discrete and continuous circles." Journal of Applied Probability 30, no. 04 (1993): 780–89. http://dx.doi.org/10.1017/s0021900200044569.

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We consider a large class of random walks on the discrete circle Z/(n), defined in terms of a piecewise Lipschitz function, and motivated by the ‘generation gap' process of Diaconis. For such walks, we show that the time until convergence to stationarity is bounded independently of n. Our techniques involve Fourier analysis and a comparison of the random walks on Z/(n) with a random walk on the continuous circle S 1.

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22

Wong, Thomas G. "Unstructured search by random and quantum walk." Quantum Information and Computation 22, no. 1&2 (2022): 53–85. http://dx.doi.org/10.26421/qic22.1-2-4.

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The task of finding an entry in an unsorted list of $N$ elements famously takes $O(N)$ queries to an oracle for a classical computer and $O(\sqrt{N})$ queries for a quantum computer using Grover's algorithm. Reformulated as a spatial search problem, this corresponds to searching the complete graph, or all-to-all network, for a marked vertex by querying an oracle. In this tutorial, we derive how discrete- and continuous-time (classical) random walks and quantum walks solve this problem in a thorough and pedagogical manner, providing an accessible introduction to how random and quantum walks can

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23

Michelitsch, Thomas M., Federico Polito, and Alejandro P. Riascos. "Biased Continuous-Time Random Walks with Mittag-Leffler Jumps." Fractal and Fractional 4, no. 4 (2020): 1–29. https://doi.org/10.3390/fractalfract4040051.

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We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has connections with biased walks on digraphs. Within this framework, we introduce a space-time generalization of the Poisson process as a strictly increasing walk with discrete Mittag-Leffler jumps time-changed with an independent (continuous-time) fractional Poisson process. We call this process ‘space-time Mittag-Leffler process’. We derive explicit formu

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24

Pozzoli, Gaia, Mattia Radice, Manuele Onofri, and Roberto Artuso. "A Continuous-Time Random Walk Extension of the Gillis Model." Entropy 22, no. 12 (2020): 1431. http://dx.doi.org/10.3390/e22121431.

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We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional non-homogeneous random walk with a position-dependent drift known in the mathematical literature as Gillis random walk. This modified stochastic process allows to significantly change local, non-local and transport properties in the presence of heavy-tailed waiting-time distributions lacking the first moment: we provide here exact results concerning hitting times, first-time events, survival probabilities, occupation times, the moments spectrum

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25

KONNO, NORIO. "CONTINUOUS-TIME QUANTUM WALKS ON ULTRAMETRIC SPACES." International Journal of Quantum Information 04, no. 06 (2006): 1023–35. http://dx.doi.org/10.1142/s0219749906002389.

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We introduce a continuous-time quantum walk on an ultrametric space corresponding to the set of p-adic integers and compute its time-averaged probability distribution. It is shown that localization occurs for any location of the ultrametric space for the walk. This result presents a striking contrast to the classical random walk case. Moreover, we clarify a difference between the ultrametric space and other graphs, such as cycle graph, line, hypercube and complete graph, for the localization of the quantum case. Our quantum walk may be useful for a quantum search algorithm on a tree-like hiera

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26

Osmekhin, Sergey, and Fr ́ed ́eric D ́el`eze. "Application of continuous - time random walk to statistical arbitrage." Journal of Engineering Science and Technology Review 8, no. 1 (2015): 91–95. http://dx.doi.org/10.25103/jestr.81.16.

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27

Böhm, W., and W. Panny. "Simple random walk statistics. Part II: Continuous time results." Journal of Applied Probability 33, no. 2 (1996): 331–39. http://dx.doi.org/10.2307/3215057.

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In this paper various statistics for randomized random walks and their distributions are presented. The distributional results are derived by means of a limiting procedure applied to the pertaining discrete time process, which has been considered in part I of this work (Katzenbeisser and Panny 1996). This basic approach, originally due to Meisling (1958), seems to offer certain technical advantages, since it avoids the use of Laplace transforms and is even simpler than Feller's randomization technique.

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28

Balescu, R. "Continuous time random walk model for standard map dynamics." Physical Review E 55, no. 3 (1997): 2465–74. http://dx.doi.org/10.1103/physreve.55.2465.

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29

Böhm, W., and W. Panny. "Simple random walk statistics. Part II: Continuous time results." Journal of Applied Probability 33, no. 02 (1996): 331–39. http://dx.doi.org/10.1017/s0021900200099757.

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In this paper various statistics for randomized random walks and their distributions are presented. The distributional results are derived by means of a limiting procedure applied to the pertaining discrete time process, which has been considered in part I of this work (Katzenbeisser and Panny 1996). This basic approach, originally due to Meisling (1958), seems to offer certain technical advantages, since it avoids the use of Laplace transforms and is even simpler than Feller's randomization technique.

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30

Schumer, Rina, Boris Baeumer, and Mark M. Meerschaert. "Extremal behavior of a coupled continuous time random walk." Physica A: Statistical Mechanics and its Applications 390, no. 3 (2011): 505–11. http://dx.doi.org/10.1016/j.physa.2010.10.018.

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31

Castro, J., and J. Rivas. "A continuous time random walk approach to magnetic disaccommodation." Journal of Magnetism and Magnetic Materials 130, no. 1-3 (1994): 342–46. http://dx.doi.org/10.1016/0304-8853(94)90692-0.

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32

FA, KWOK SAU, and K. G. WANG. "INTEGRO-DIFFERENTIAL EQUATIONS ASSOCIATED WITH CONTINUOUS-TIME RANDOM WALK." International Journal of Modern Physics B 27, no. 12 (2013): 1330006. http://dx.doi.org/10.1142/s0217979213300065.

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The continuous-time random walk (CTRW) model is a useful tool for the description of diffusion in nonequilibrium systems, which is broadly applied in nature and life sciences, e.g., from biophysics to geosciences. In particular, the integro-differential equations for diffusion and diffusion-advection are derived asymptotically from the decoupled CTRW model and a generalized Chapmann–Kolmogorov equation, with generic waiting time probability density function (PDF) and external force. The advantage of the integro-differential equations is that they can be used to investigate the entire diffusion

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33

Escaff, Daniel, Raúl Toral, Christian Van den Broeck, and Katja Lindenberg. "A continuous-time persistent random walk model for flocking." Chaos: An Interdisciplinary Journal of Nonlinear Science 28, no. 7 (2018): 075507. http://dx.doi.org/10.1063/1.5027734.

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34

Miyazaki, S., T. Harada, and A. Budiyono. "Continuous-Time Random Walk Approach to On-Off Diffusion." Progress of Theoretical Physics 106, no. 6 (2001): 1051–78. http://dx.doi.org/10.1143/ptp.106.1051.

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35

Liu, Jian, and Jing-Dong Bao. "Effective Jump Length of Coupled Continuous Time Random Walk." Chinese Physics Letters 30, no. 2 (2013): 020202. http://dx.doi.org/10.1088/0256-307x/30/2/020202.

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36

Masoliver, Jaume, Miquel Montero, Josep Perelló, and George H. Weiss. "The continuous time random walk formalism in financial markets." Journal of Economic Behavior & Organization 61, no. 4 (2006): 577–98. http://dx.doi.org/10.1016/j.jebo.2004.07.015.

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37

Masoliver, Jaume, Katja Lindenberg, and George H. Weiss. "A continuous-time generalization of the persistent random walk." Physica A: Statistical Mechanics and its Applications 157, no. 2 (1989): 891–98. http://dx.doi.org/10.1016/0378-4371(89)90071-x.

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38

FA, KWOK SAU. "CONTINUOUS-TIME FINANCE AND THE WAITING TIME DISTRIBUTION: MULTIPLE CHARACTERISTIC TIMES." Modern Physics Letters B 26, no. 23 (2012): 1250151. http://dx.doi.org/10.1142/s0217984912501515.

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In this paper, we model the tick-by-tick dynamics of markets by using the continuous-time random walk (CTRW) model. We employ a sum of products of power law and stretched exponential functions for the waiting time probability distribution function; this function can fit well the waiting time distribution for BUND futures traded at LIFFE in 1997.

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39

Richter, Susanne, and Günter Vojta. "Generalized non-Markovian master equation for continuous time random walk with random flying times." Physica A: Statistical Mechanics and its Applications 188, no. 4 (1992): 631–43. http://dx.doi.org/10.1016/0378-4371(92)90335-n.

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40

Liu, Jian, Bao-He Li, and Xiao-Song Chen. "Generalized Master Equation for Space-Time Coupled Continuous Time Random Walk." Chinese Physics Letters 34, no. 5 (2017): 050201. http://dx.doi.org/10.1088/0256-307x/34/5/050201.

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41

Liu, Jian, and Jing-Dong Bao. "Continuous time random walk with jump length correlated with waiting time." Physica A: Statistical Mechanics and its Applications 392, no. 4 (2013): 612–17. http://dx.doi.org/10.1016/j.physa.2012.10.019.

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42

Michelitsch, Thomas M., Federico Polito, and Alejandro P. Riascos. "Biased Continuous-Time Random Walks with Mittag-Leffler Jumps." Fractal and Fractional 4, no. 4 (2020): 51. http://dx.doi.org/10.3390/fractalfract4040051.

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Abstract:

We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has connections with biased walks on digraphs. Within this framework, we introduce a space-time generalization of the Poisson process as a strictly increasing walk with discrete Mittag-Leffler jumps time-changed with an independent (continuous-time) fractional Poisson process. We call this process ‘space-time Mittag-Leffler process’. We derive explicit formulae for the

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43

AGLIARI, ELENA, OLIVER MÜLKEN, and ALEXANDER BLUMEN. "CONTINUOUS-TIME QUANTUM WALKS AND TRAPPING." International Journal of Bifurcation and Chaos 20, no. 02 (2010): 271–79. http://dx.doi.org/10.1142/s0218127410025715.

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Recent findings suggest that processes such as the excitonic energy transfer through the photosynthetic antenna display quantal features, aspects known from the dynamics of charge carriers along polymer backbones. Hence, in modeling energy transfer one has to leave the classical, master-equation-type formalism and advance towards an increasingly quantum-mechanical picture, while still retaining a local description of the complex network of molecules involved in the transport, say through a tight-binding approach. Interestingly, the continuous time random walk (CTRW) picture, widely employed in

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44

Nicolau, João. "STATIONARY PROCESSES THAT LOOK LIKE RANDOM WALKS— THE BOUNDED RANDOM WALK PROCESS IN DISCRETE AND CONTINUOUS TIME." Econometric Theory 18, no. 1 (2002): 99–118. http://dx.doi.org/10.1017/s0266466602181060.

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Several economic and financial time series are bounded by an upper and lower finite limit (e.g., interest rates). It is not possible to say that these time series are random walks because random walks are limitless with probability one (as time goes to infinity). Yet, some of these time series behave just like random walks. In this paper we propose a new approach that takes into account these ideas. We propose a discrete-time and a continuous-time process (diffusion process) that generate bounded random walks. These paths are almost indistinguishable from random walks, although they are stocha

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45

Lin Fang and Bao Jing-Dong. "Approach of continuous time random walk model to anomalous diffusion." Acta Physica Sinica 57, no. 2 (2008): 696. http://dx.doi.org/10.7498/aps.57.696.

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46

Johnson, Devin S., Joshua M. London, Mary-Anne Lea, and John W. Durban. "CONTINUOUS-TIME CORRELATED RANDOM WALK MODEL FOR ANIMAL TELEMETRY DATA." Ecology 89, no. 5 (2008): 1208–15. http://dx.doi.org/10.1890/07-1032.1.

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47

Gubiec, T., and R. Kutner. "Share Price Evolution as Stationary, Dependent Continuous-Time Random Walk." Acta Physica Polonica A 117, no. 4 (2010): 669–72. http://dx.doi.org/10.12693/aphyspola.117.669.

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48

Rodríguez-Romo, Suemi, and Vladimir Tchijov. "On Continuous-Time Self-Avoiding Random Walk in Dimension Four." Journal of Statistical Physics 90, no. 3-4 (1998): 767–81. http://dx.doi.org/10.1023/a:1023276920343.

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49

Barkai, E., and I. M. Sokolov. "Multi-point distribution function for the continuous time random walk." Journal of Statistical Mechanics: Theory and Experiment 2007, no. 08 (2007): P08001. http://dx.doi.org/10.1088/1742-5468/2007/08/p08001.

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50

Nelson, Jenny. "Continuous-time random-walk model of electron transport in nanocrystallineTiO2electrodes." Physical Review B 59, no. 23 (1999): 15374–80. http://dx.doi.org/10.1103/physrevb.59.15374.

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