A Method for Analyzing Backward Recurrence Time Data on Residential Mobility

1988 ◽  
Vol 18 ◽  
pp. 105 ◽  
Author(s):  
Nazli Baydar ◽  
Michael White
Keyword(s):  
Residential Mobility ◽  
Recurrence Time ◽  
Time Data ◽  
Backward Recurrence Time

Semiparametric inference with correlated recurrence time data

2013 ◽  
Vol 10 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Akim Adekpedjou ◽  
Jonathan Quiton ◽  
Xuerong Meggie Wen
Keyword(s):  
Recurrence Time ◽  
Time Data ◽  
Semiparametric Inference

Critical growth of a semi-linear process

2004 ◽  
Vol 41 (2) ◽  
pp. 355-367
Author(s):  
Ilya Molchanov ◽  
Vadim Shcherbakov ◽  
Sergei Zuyev
Keyword(s):  
Renewal Process ◽  
Survival Probability ◽  
Linear Process ◽  
Recurrence Time ◽  
Soil Drying ◽  
Time Process ◽  
Positive Probability ◽  
Drying Process ◽  
Dry Patch ◽  
Backward Recurrence Time

This paper is motivated by the modelling of leaching of bacteria through soil. A semi-linear process Xt− may be used to describe the soil-drying process between rain showers. This is a backward recurrence time process that corresponds to the renewal process of instances of rain. If a bacterium moves according to another process h, then the fact that h(t) stays above Xt− means that the bacterium never hits a dry patch of soil and so survives. We describe a critical behaviour of h that separates the cases when survival is possible with a positive probability from the cases when this probability vanishes. An explicit formula for the survival probability is obtained in case h is linear and rain showers follow a Poisson process.

scholarly journals Strong Earthquakes Recurrence Times of the Southern Thessaly, Greece, Fault System: Insights from a Physics-Based Simulator Application

2021 ◽  
Vol 9 ◽  
Author(s):  
Christos Kourouklas ◽  
Rodolfo Console ◽  
Eleftheria Papadimitriou ◽  
Maura Murru ◽  
Vassilios Karakostas
Keyword(s):  
Detailed Examination ◽  
Passage Time ◽  
Fault System ◽  
Recurrence Time ◽  
Time Data ◽  
Strong Earthquakes ◽  
Earthquake Catalogs ◽  
Long Duration ◽  
Major Fault ◽  
Recurrence Behavior

The recurrence time, Tr, of strong earthquakes above a predefined magnitude threshold on specific faults or fault segments is an important parameter, that could be used as an input in the development of long-term fault-based Earthquake Rupture Forecasts (ERF). The amount of observational recurrence time data per segment is often limited, due to the long duration of the stress rebuilt and the shortage of earthquake catalogs. As a consequence, the application of robust statistical models is difficult to implement with a precise conclusion, concerning Tr and its variability. Physics-based earthquake simulators are a powerful tool to overcome these limitations, and could provide much longer earthquake records than the historical and instrumental earthquake catalogs. A physics-based simulator, which embodies known physical processes, is applied in the Southern Thessaly Fault Zone (Greece), aiming to provide insights about the recurrence behavior of earthquakes with Mw ≥ 6.0 in the six major fault segments in the study area. The build of the input fault model is made by compiling the geometrical and kinematic parameters of the fault network from the available seismotectonic studies. The simulation is implemented through the application of the algorithm multiple times, with a series of different input free parameters, in order to conclude in the simulated catalog which showed the best performance in respect to the observational data. The detailed examination of the 254 Mw ≥ 6.0 earthquakes reported in the simulated catalog reveals that both single and multiple segmented ruptures can be realized in the study area. Results of statistical analysis of the interevent times of the Mw ≥ 6.0 earthquakes per segment evidence quasi-periodic recurrence behavior and better performance of the Brownian Passage Time (BPT) renewal model in comparison to the Poissonian behavior.

Critical growth of a semi-linear process

2004 ◽  
Vol 41 (02) ◽  
pp. 355-367
Author(s):  
Ilya Molchanov ◽  
Vadim Shcherbakov ◽  
Sergei Zuyev
Keyword(s):  
Renewal Process ◽  
Survival Probability ◽  
Linear Process ◽  
Recurrence Time ◽  
Soil Drying ◽  
Time Process ◽  
Positive Probability ◽  
Drying Process ◽  
Dry Patch ◽  
Backward Recurrence Time

This paper is motivated by the modelling of leaching of bacteria through soil. A semi-linear process X t − may be used to describe the soil-drying process between rain showers. This is a backward recurrence time process that corresponds to the renewal process of instances of rain. If a bacterium moves according to another process h, then the fact that h(t) stays above X t − means that the bacterium never hits a dry patch of soil and so survives. We describe a critical behaviour of h that separates the cases when survival is possible with a positive probability from the cases when this probability vanishes. An explicit formula for the survival probability is obtained in case h is linear and rain showers follow a Poisson process.

Two mean values which characterize the Poisson process

1973 ◽  
Vol 10 (3) ◽  
pp. 678-681 ◽  
Author(s):  
Erhan Çinlar ◽  
Peter Jagers
Keyword(s):  
Poisson Process ◽  
Renewal Process ◽  
Recurrence Time ◽  
Mean Values ◽  
The Mean ◽  
Forward Recurrence Time ◽  
Backward Recurrence Time ◽  
Interval Distribution

The Poisson process enjoys two special properties: the mean forward recurrence time at time t does not depend on t, and the mean backward recurrence time at time t is the “mean” of the interval distribution truncated at t. Poisson process is the only renewal process with these properties.

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