Transformation of time dependent probability distributions

2009 ◽  
Author(s):  
Juraj Tekel ◽  
Leon Cohen
Keyword(s):  
Probability Distributions ◽  
Time Dependent ◽  
Dependent Probability

scholarly journals Probability Representation of Quantum Mechanics Where System States Are Identified with Probability Distributions

2020 ◽  
Vol 2 (1) ◽  
pp. 64-79 ◽  
Author(s):  
Vladimir Chernega ◽  
Olga Man'ko ◽  
Vladimir Man'ko
Keyword(s):  
Quantum Mechanics ◽  
Probability Distributions ◽  
Random Variables ◽  
Time Dependent ◽  
Continuous Variables ◽  
Probability Representation ◽  
Classical Statistics ◽  
Quantum Observables ◽  
System States ◽  
Dependent Probability

The probability representation of quantum mechanics where the system states are identified with fair probability distributions is reviewed for systems with continuous variables (the example of the oscillator) and discrete variables (the example of the qubit). The relation for the evolution of the probability distributions which determine quantum states with the Feynman path integral is found. The time-dependent phase of the wave function is related to the time-dependent probability distribution which determines the density matrix. The formal classical-like random variables associated with quantum observables for qubit systems are considered, and the connection of the statistics of the quantum observables with the classical statistics of the random variables is discussed.

Quantifying electron transit in donor-bridge-acceptor systems using probabilistic confidence

2018 ◽  
Vol 17 (07) ◽  
pp. 1850046 ◽  
Author(s):  
Evan Curtin ◽  
Gloria Bazargan ◽  
Karl Sohlberg
Keyword(s):  
Charge Transport ◽  
Conditional Probability ◽  
Probabilistic Approach ◽  
Probability Analysis ◽  
Time Dependent ◽  
Quantum Particles ◽  
Transit Times ◽  
Conditional Probability Analysis ◽  
Insight Into ◽  
Dependent Probability

A probabilistic approach to characterizing transit times for quantum particles is generalized to a system of more than two spatial regions and applied to the transport of charge in donor-bridge-acceptor systems. The approach is based on applying conditional probability analysis to a discrete representation of the time-dependent probability density as generated by numerical solution of the time-dependent Schrödinger equation for an initially localized electron. To carry out this analysis, it is first necessary to cast the conditional probability analysis approach in matrix form. The results afford a quantification of the electron transit time and may provide a tool to gain insight into the mechanism of charge transport.

scholarly journals SIGNIFICANT EARTHQUAKES NEAR THE CITY OF THESSALONIKI (NORTHERN GREECE) AND PROBABILITY DISTRIBUTION ON FAULTS

2017 ◽  
Vol 50 (3) ◽  
pp. 1389
Author(s):  
P.M. Paradisopoulou ◽  
E.E. Papadimitriou ◽  
J. Mirek
Keyword(s):  
Stress Transfer ◽  
Time Dependent ◽  
Earthquake Catalog ◽  
Northern Greece ◽  
Earthquake Probability ◽  
Fault Segment ◽  
Probability Estimates ◽  
Macroseismic Intensities ◽  
The City ◽  
Dependent Probability

Stress triggering must be incorporated into quantitative earthquake probability estimate, given that faults are interacted though their stress field. Using time dependent probability estimates this work aims at the evaluation of the occurrence probability of anticipated earthquakes near the city of Thessaloniki, an urban center of 1 million people located in northern Greece, conditional to the time elapsed since the last stronger event on each fault segment of the study area. A method that calculates the macroseismic epicenter and magnitude according to macroseismic intensities is used to improve the existing earthquake catalog (from AD 1600 - 2013 with M≥6.0) in order to compute new interevent and elapsed time values which form the basis for time-dependent probability estimates. To investigate the effects of stress transfer to seismic hazard, the probabilistic calculations presented here employ detailed models of coseismic stress associated with the 20 June 1978 M=6.5 Thessaloniki which is the latest destructive earthquake in the area in the instrumental era. The combined 2015-2045 regional Poisson probability of M≥6.0 earthquakes is ~35% the regional time-dependent probability varies from 0% to 15% and incorporation of stress transfer from 0% to 20% for each fault segment.

Analysis of Feedback Retrial Queue with Starting Failure and Server Vacation

2016 ◽  
pp. 71-96
Author(s):  
K. Sathiya Thiyagarajan ◽  
G. Ayyappan
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Generating Functions ◽  
Retrial Queue ◽  
Laplace Transforms ◽  
Time Dependent ◽  
Steady State Analysis ◽  
Starting Failure ◽  
Dependent Probability ◽  
Bernoulli Vacation

In this chapter we discusses a batch arrival feedback retrial queue with Bernoulli vacation, where the server is subjected to starting failure. Any arriving batch finding the server busy, breakdown or on vacation enters an orbit. Otherwise one customer from the arriving batch enters a service immediately while the rest join the orbit. After the completion of each service, the server either goes for a vacation with probability or may wait for serving the next customer. Repair times, service times and vacation times are assumed to be arbitrarily distributed. The time dependent probability generating functions have been obtained in terms of their Laplace transforms. The steady state analysis and key performance measures of the system are also studied. Finally, some numerical illustrations are presented.

Time-Dependent Reliability Analysis of Vibratory Systems With Random Parameters

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Zissimos P. Mourelatos ◽  
Monica Majcher ◽  
Vasileios Geroulas
Keyword(s):  
Large Scale ◽  
Probability Of Failure ◽  
Time Dependent ◽  
Total Probability ◽  
Conditional Probabilities ◽  
Random Parameters ◽  
Random Vibrations ◽  
Input Parameters ◽  
Total Probability Theorem ◽  
Dependent Probability

The field of random vibrations of large-scale systems with millions of degrees-of-freedom (DOF) is of significant importance in many engineering disciplines. In this paper, we propose a method to calculate the time-dependent reliability of linear vibratory systems with random parameters excited by nonstationary Gaussian processes. The approach combines principles of random vibrations, the total probability theorem, and recent advances in time-dependent reliability using an integral equation involving the upcrossing and joint upcrossing rates. A space-filling design, such as optimal symmetric Latin hypercube (OSLH) sampling, is first used to sample the input parameter space. For each design point, the corresponding conditional time-dependent probability of failure is calculated efficiently using random vibrations principles to obtain the statistics of the output process and an efficient numerical estimation of the upcrossing and joint upcrossing rates. A time-dependent metamodel is then created between the input parameters and the output conditional probabilities allowing us to estimate the conditional probabilities for any set of input parameters. The total probability theorem is finally applied to calculate the time-dependent probability of failure. The proposed method is demonstrated using a vibratory beam example.

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