Modeling share price evolution as a continuous time random walk (CTRW) with non-independent price changes and waiting times

2004 ◽  
Vol 344 (1-2) ◽  
pp. 108-111 ◽  
Author(s):  
Przemysław Repetowicz ◽  
Peter Richmond
Keyword(s):  
Random Walk ◽  
Continuous Time ◽  
Waiting Times ◽  
Continuous Time Random Walk ◽  
Share Price ◽  
Price Changes

scholarly journals Chover-Type Laws of the Iterated Logarithm for Continuous Time Random Walks

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Kyo-Shin Hwang ◽  
Wensheng Wang
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Anomalous Diffusion ◽  
Renewal Process ◽  
Continuous Time ◽  
Waiting Times ◽  
Continuous Time Random Walk ◽  
Domains Of Attraction ◽  
Iterated Logarithm ◽  
Continuous Time Random Walks

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.

scholarly journals Generalized Diffusion Equation Associated with a Power-Law Correlated Continuous Time Random Walk

2019 ◽  
Vol 2019 ◽  
pp. 1-5
Author(s):  
Long Shi
Keyword(s):  
Random Walk ◽  
Diffusion Equation ◽  
Power Law ◽  
Continuous Time ◽  
Continuum Limit ◽  
Waiting Times ◽  
Mean Square Displacement ◽  
Continuous Time Random Walk ◽  
Mean Square ◽  
The Mean

In this work, a generalization of continuous time random walk is considered, where the waiting times among the subsequent jumps are power-law correlated with kernel function M(t)=tρ(ρ>-1). In a continuum limit, the correlated continuous time random walk converges in distribution a subordinated process. The mean square displacement of the proposed process is computed, which is of the form 〈x2(t)〉∝tH=t1/(1+ρ+1/α). The anomy exponent H varies from α to α/(1+α) when -1<ρ<0 and from α/(1+α) to 0 when ρ>0. The generalized diffusion equation of the process is also derived, which has a unified form for the above two cases.

scholarly journals Large Deviations for Continuous Time Random Walks

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 697 ◽  
Author(s):  
Wanli Wang ◽  
Eli Barkai ◽  
Stanislav Burov
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Exponential Decay ◽  
Continuous Time ◽  
Large Deviation ◽  
Waiting Times ◽  
Continuous Time Random Walk ◽  
Random Walk Model ◽  
Logarithmic Correction ◽  
Continuous Time Random Walks

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 times, the spreading of particles follows an exponential decay at large distances, with a logarithmic correction. Here we show how anti-bunching of jump events reduces the effect, while bunching and intermittency enhances it. We employ exact solutions of the continuous time random walk model to test the large deviation theory.

scholarly journals Continuous-time random walk with correlated waiting times

2009 ◽  
Vol 80 (3) ◽  
Author(s):  
Aleksei V. Chechkin ◽  
Michael Hofmann ◽  
Igor M. Sokolov
Keyword(s):  
Random Walk ◽  
Continuous Time ◽  
Waiting Times ◽  
Continuous Time Random Walk

An investigation on continuous time random walk model for bedload transport

2019 ◽  
Vol 22 (6) ◽  
pp. 1480-1501 ◽  
Author(s):  
ZhiPeng Li ◽  
HongGuang Sun ◽  
Renat T. Sibatov
Keyword(s):  
Random Walk ◽  
Diffusion Equation ◽  
Continuous Time ◽  
Waiting Times ◽  
Bedload Transport ◽  
Continuous Time Random Walk ◽  
Random Walk Model ◽  
Advection Diffusion Equation ◽  
Normal Diffusion ◽  
Heavy Tailed

Abstract Bedload particles in the armoring layer may experience a multi-scale effect and multiple mass transfer rates between mobile and immobile domains. Anomalous transport behaviors and retarded space evolution plume cannot be described by the normal diffusion equation. In this paper, we apply the continuous time random walk model with different distributions of waiting times to capture bedload transport behavior under different conditions. Experimental data indicate that fluctuations of diffusive rates for bedload transport can be captured by the truncated power law (TPL). The retarded plume evolution can be well characterized by an exponential distribution of waiting times and advection-diffusion equation with a retarded kernel. The heavy-tailed snapshots of bedload transport are interpreted in terms of mobile and immobile states.

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