Strong convergence of multivariate point processes of exceedances

1993 ◽  
Vol 45 (3) ◽  
pp. 433-444 ◽  
Author(s):  
E. Kaufmann ◽  
R. -D. Reiss
Keyword(s):  
Strong Convergence ◽  
Point Processes ◽  
Multivariate Point ◽  
Multivariate Point Processes

An application of multivariate point processes in teletraffic systems

1979 ◽  
Vol 11 (2) ◽  
pp. 274-274
Author(s):  
D. R. Manfield ◽  
T. Downs
Keyword(s):  
Point Processes ◽  
Multivariate Point ◽  
Multivariate Point Processes

Orderliness, intensities and Palm-Khinchin equations for multivariate point processes

1975 ◽  
Vol 12 (2) ◽  
pp. 383-389 ◽  
Author(s):  
D. J. Daley ◽  
R. K. Milne
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Multivariate Point ◽  
Multivariate Point Processes

Simple definitions and derivations of elementary properties are given for the various intensities and Palm-Khinchin functions associated with a multivariate point process.

Multivariate Point Processes

1972 ◽  
pp. 401-448
Author(s):  
D. R. Cox ◽  
P. A. W. Lewis
Keyword(s):  
Point Processes ◽  
Multivariate Point ◽  
Multivariate Point Processes

Regenerative multivariate point processes

1978 ◽  
Vol 10 (2) ◽  
pp. 411-430 ◽  
Author(s):  
Mark Berman
Keyword(s):  
General Theory ◽  
Asymptotic Behaviour ◽  
Generating Function ◽  
Point Processes ◽  
Probability Generating Function ◽  
Joint Probability ◽  
Fixed Length ◽  
Multivariate Point ◽  
Monotonicity Results ◽  
Multivariate Point Processes

A class of stationary multivariate point processes is considered in which the events of one of the point processes act as regeneration points for the entire multivariate process. Some important properties of such processes are derived including the joint probability generating function for numbers of events in an interval of fixed length and the asymptotic behaviour of such processes. The general theory is then applied in three bivariate examples. Finally, some simple monotonicity results for stationary and renewal point processes (which are used in the second example) are proved in two appendices.

Multivariate point processes

2018 ◽  
pp. 117-142 ◽  
Author(s):  
D.R. cox ◽  
Valerie Isham
Keyword(s):  
Point Processes ◽  
Multivariate Point ◽  
Multivariate Point Processes

Learning models with continuous time parameter and multivariate point processes

1983 ◽  
Vol 20 (4) ◽  
pp. 884-890 ◽  
Author(s):  
Helmut Pruscha
Keyword(s):  
Point Process ◽  
Continuous Time ◽  
Point Processes ◽  
Transition Probabilities ◽  
Learning Model ◽  
Time Parameter ◽  
Learning Models ◽  
Random System ◽  
Multivariate Point ◽  
Multivariate Point Processes

The concept of a learning model (or random system with complete connections) with continuous time parameter is introduced on the basis of the notion of a multivariate point process possessing an intensity. The stepwise transition probabilities in terms of the intensity are derived and a Monte Carlo method for simulating a sample is presented. By modelling the intensity process various types of learning models can be built. We propose a linear learning model which comprises the continuous-time Markov process as well as Hawkes's mutually exciting point process. We study the asymptotic behaviour of this linear model in terms of explosion or extinction and of convergence of some estimates. We close with some numerical results from computer simulations.

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