scholarly journals Absorption Time Distribution for an Asymmetric Random Walk

2008 ◽  
pp. 31-40
Author(s):  
S. N. Ethier
Keyword(s):  
Random Walk ◽  
Time Distribution ◽  
Absorption Time

CONTINUOUS-TIME FINANCE AND THE WAITING TIME DISTRIBUTION: MULTIPLE CHARACTERISTIC TIMES

2012 ◽  
Vol 26 (23) ◽  
pp. 1250151 ◽  
Author(s):  
KWOK SAU FA
Keyword(s):  
Distribution Function ◽  
Random Walk ◽  
Waiting Time ◽  
Continuous Time ◽  
Probability Distribution Function ◽  
Time Distribution ◽  
Waiting Time Distribution ◽  
Exponential Functions ◽  
Multiple Characteristic ◽  
Sum Of Products

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.

Moments of Absorption Time for a Conditioned Random Walk

1979 ◽  
Vol 60 (1) ◽  
pp. 83-90 ◽  
Author(s):  
W. A. Beyer ◽  
M.S. Waterman
Keyword(s):  
Random Walk ◽  
Absorption Time

On the maximum and absorption time of left-continuous random walk

1978 ◽  
Vol 15 (2) ◽  
pp. 292-299 ◽  
Author(s):  
Anthony G. Pakes
Keyword(s):  
Random Walk ◽  
Limit Theorems ◽  
Initial Position ◽  
Absorption Time ◽  
Conditional Limit Theorems ◽  
Negative Drift ◽  
Continuous Random Walk ◽  
Conditional Limit ◽  
Transformed Distribution

In a recent paper Green (1976) obtained some conditional limit theorems for the absorption time of left-continuous random walk. His methods require that in the driftless case the increment distribution has exponentially decreasing tails and that the same is true for a transformed distribution in the case of negative drift.Here we take a different approach which will produce Green's results under minimal conditions. Limit theorems are given for the maximum as the initial position of the random walk tends to infinity.

scholarly journals Quantifying time-variant travel time distribution by multi-fidelity model in hillslope under nonstationary hydrologic conditions

2021 ◽  
Author(s):  
Rong Mao ◽  
Jiu Jimmy Jiao ◽  
Xin Luo ◽  
Hailong Li
Keyword(s):  
Random Walk ◽  
Travel Time ◽  
Particle Tracking ◽  
Time Distribution ◽  
High Fidelity ◽  
Mixing Process ◽  
Particle Tracking Model ◽  
Travel Time Distribution ◽  
Tracking Model ◽  
Fidelity Model

Abstract. The travel time distribution (TTD) is a lumped representation of groundwater discharge and solute export responding to rainfall. It reflects the mixing process of water parcels and solute particles of different ages and characterizes reactive transport progress in hillslope aquifers. As a result of the mixing process, groundwater leaving the system at a certain time is an integration of multiple water parcels of different ages from different historical rainfall events. Under nonstationary rainfall input condition, the TTD varies with transit groundwater flow, leading to the time-variant TTD. Most methods for estimating time-variant TTD are constrained by requiring either the long-term continuous hydrogeochemical data or the intensive computations. This study introduces a multi-fidelity model to overcome these limitations and evaluate time-variant TTD numerically. In this multi-fidelity model, groundwater age distribution model is taken as the high-fidelity model, and particle tracking model without random walk is taken as the low-fidelity model. Non-parametric regression by non-linear Gaussian process is applied to correlate the two models and then build up the multi-fidelity model. The advantage of the multi-fidelity model is that it combines the accuracy of high-fidelity model and the computational efficiency of low-fidelity model. Moreover, in groundwater and solute transport model with low P\\'eclet number, as the spatial scale of the model increases, the number of particles required for multi-fidelity model is reduced significantly compared to random walk particle tracking model. The correlation between high and low-fidelity models is demonstrated in a one dimensional pulse injection case. In a two dimensional hypothetical model, convergence analysis indicates that the multi-fidelity model converges well when increasing the number of high-fidelity models. Error analysis also confirms the good performance of the multi-fidelity model.

First-passage-time distribution in a random random walk

1990 ◽  
Vol 42 (4) ◽  
pp. 2047-2064 ◽  
Author(s):  
S. H. Noskowicz ◽  
I. Goldhirsch
Keyword(s):  
Random Walk ◽  
Time Distribution ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage

Asymptotic expansion of the absorption-time distribution for a markov chain

Cybernetics ◽  
1975 ◽  
Vol 9 (4) ◽  
pp. 694-697
Author(s):  
V. S. Korolyuk ◽  
I. P. Penev ◽  
A. F. Turbin
Keyword(s):  
Asymptotic Expansion ◽  
Markov Chain ◽  
Time Distribution ◽  
Absorption Time
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