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Gotowe bibliografie tematyczne / Continuous Time Random Walk (CTRW)

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Artykuły w czasopismach

Gotowa bibliografia na temat „Continuous Time Random Walk (CTRW)”

Autor: Grafiati

Data publikacji: 6 września 2023

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Artykuły w czasopismach na temat "Continuous Time Random Walk (CTRW)"

1

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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2

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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3

Jara, M., and T. Komorowski. "Limit theorems for some continuous-time random walks." Advances in Applied Probability 43, no. 3 (2011): 782–813. http://dx.doi.org/10.1239/aap/1316792670.

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In this paper we consider the scaled limit of a continuous-time random walk (CTRW) based on a Markov chain {Xn,n≥ 0} and two observables, τ(∙) andV(∙), corresponding to the renewal times and jump sizes. Assuming that these observables belong to the domains of attraction of some stable laws, we give sufficient conditions on the chain that guarantee the existence of the scaled limits for CTRWs. An application of the results to a process that arises in quantum transport theory is provided. The results obtained in this paper generalize earlier results contained in Becker-Kern, Meerschaert and Sche

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4

Jara, M., and T. Komorowski. "Limit theorems for some continuous-time random walks." Advances in Applied Probability 43, no. 03 (2011): 782–813. http://dx.doi.org/10.1017/s0001867800005140.

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In this paper we consider the scaled limit of a continuous-time random walk (CTRW) based on a Markov chain {X n , n ≥ 0} and two observables, τ(∙) and V(∙), corresponding to the renewal times and jump sizes. Assuming that these observables belong to the domains of attraction of some stable laws, we give sufficient conditions on the chain that guarantee the existence of the scaled limits for CTRWs. An application of the results to a process that arises in quantum transport theory is provided. The results obtained in this paper generalize earlier results contained in Becker-Kern, Meerschaert and

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5

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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6

Weron, Karina, Aleksander Stanislavsky, Agnieszka Jurlewicz, Mark M. Meerschaert, and Hans-Peter Scheffler. "Clustered continuous-time random walks: diffusion and relaxation consequences." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2142 (2012): 1615–28. http://dx.doi.org/10.1098/rspa.2011.0697.

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We present a class of continuous-time random walks (CTRWs), in which random jumps are separated by random waiting times. The novel feature of these CTRWs is that the jumps are clustered. This introduces a coupled effect, with longer waiting times separating larger jump clusters. We show that the CTRW scaling limits are time-changed processes. Their densities solve two different fractional diffusion equations, depending on whether the waiting time is coupled to the preceding jump, or the following one. These fractional diffusion equations can be used to model all types of experimentally observe

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7

MAINARDI, FRANCESCO, ALESSANDRO VIVOLI, and RUDOLF GORENFLO. "CONTINUOUS TIME RANDOM WALK AND TIME FRACTIONAL DIFFUSION: A NUMERICAL COMPARISON BETWEEN THE FUNDAMENTAL SOLUTIONS." Fluctuation and Noise Letters 05, no. 02 (2005): L291—L297. http://dx.doi.org/10.1142/s0219477505002677.

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We consider the basic models for anomalous transport provided by the integral equation for continuous time random walk (CTRW) and by the time fractional diffusion equation to which the previous equation is known to reduce in the diffusion limit. We compare the corresponding fundamental solutions of these equations, in order to investigate numerically the increasing quality of approximation with advancing time.

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8

Kolokoltsov, Vassili. "CTRW modeling of quantum measurement and fractional equations of quantum stochastic filtering and control." Fractional Calculus and Applied Analysis 25, no. 1 (2022): 128–65. http://dx.doi.org/10.1007/s13540-021-00002-2.

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AbstractInitially 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 branches of modern physics it became popular to extend random walk modeling to the continuous time random walk (CTRW) modeling, where the time between discrete events is taken to be non-exponential. In the present paper we apply the CTRW modeling to the continuous quantum measurements yielding the new fractional in time evolution equations of quantum filter

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9

Abdel-Rehim, Enstar A. "From power laws to fractional diffusion processes with and without external forces, the non direct way." Fractional Calculus and Applied Analysis 22, no. 1 (2019): 60–77. http://dx.doi.org/10.1515/fca-2019-0004.

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Abstract In this paper, a wide view on the theory of the continuous time random walk (CTRW) and its relations to the space–time fractional diffusion process is given. We begin from the basic model of CTRW (Montroll and Weiss [19], 1965) that also can be considered as a compound renewal process. We are interested in studying the random walks in which the probability distributions of the waiting times and jumps have fat tails characterized by power laws with exponent between 0 and 1 for the waiting times, between 0 and 2 for the jumps. We prove the relation between the integral equation of the C

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10

Klamut, Jarosław, and Tomasz Gubiec. "Continuous Time Random Walk with Correlated Waiting Times. The Crucial Role of Inter-Trade Times in Volatility Clustering." Entropy 23, no. 12 (2021): 1576. http://dx.doi.org/10.3390/e23121576.

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In many physical, social, and economic phenomena, we observe changes in a studied quantity only in discrete, irregularly distributed points in time. The stochastic process usually applied to describe this kind of variable is the continuous-time random walk (CTRW). Despite the popularity of these types of stochastic processes and strong empirical motivation, models with a long-term memory within the sequence of time intervals between observations are rare in the physics literature. Here, we fill this gap by introducing a new family of CTRWs. The memory is introduced to the model by assuming tha

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