Some non-stationary point processes with stationary forward recurrence time distribution

1975 ◽  
Vol 12 (1) ◽  
pp. 167-169 ◽  
Author(s):  
Mats Rudemo
Keyword(s):  
Stationary Point ◽  
Time Distribution ◽  
Point Processes ◽  
Recurrence Time ◽  
Renewal Processes ◽  
Forward Recurrence Time ◽  
Stationary Point Processes

Examples are given of point processes that are non-stationary but have stationary forward recurrence time distributions. They are obtained by modification of stationary Poisson and renewal processes.

Some non-stationary point processes with stationary forward recurrence time distribution

1975 ◽  
Vol 12 (01) ◽  
pp. 167-169
Author(s):  
Mats Rudemo
Keyword(s):  
Stationary Point ◽  
Time Distribution ◽  
Point Processes ◽  
Recurrence Time ◽  
Renewal Processes ◽  
Forward Recurrence Time ◽  
Stationary Point Processes

Examples are given of point processes that are non-stationary but have stationary forward recurrence time distributions. They are obtained by modification of stationary Poisson and renewal processes.

scholarly journals The square-wave spectral density of a stationary renewal process

1989 ◽  
Vol 2 (2) ◽  
pp. 117-130 ◽  
Author(s):  
Marcel F. Neuts ◽  
H. Sitaraman
Keyword(s):  
Qualitative Study ◽  
Spectral Density ◽  
Renewal Process ◽  
Stationary Point ◽  
Point Processes ◽  
Renewal Processes ◽  
Square Wave ◽  
Promising Tool ◽  
Power Spectral ◽  
Stationary Point Processes

The power spectral density of a random square wave is a promising tool in the qualitative study of stationary point processes. This is illustrated for renewal processes and their superpositions.

On projected thick sections of stationary point processes and Boolean models

1996 ◽  
Vol 28 (2) ◽  
pp. 335-335
Author(s):  
Markus Kiderlen
Keyword(s):  
Point Process ◽  
Stationary Point ◽  
Point Processes ◽  
Linear Subspace ◽  
Isotropic Case ◽  
Thick Section ◽  
Boolean Models ◽  
Dimensional Linear Subspace ◽  
Stationary Point Process ◽  
Stationary Point Processes

For a stationary point process X of convex particles in ℝd the projected thick section process X(L) on a q-dimensional linear subspace L is considered. Formulae connecting geometric functionals, e.g. the quermass densities of X and X(L), are presented. They generalize the classical results of Miles (1976) and Davy (1976) which hold only in the isotropic case.

Bivariate stationary point processes, fundamental relations and first recurrence times

1972 ◽  
Vol 4 (02) ◽  
pp. 296-317 ◽  
Author(s):  
T. K. M. Wisniewski
Keyword(s):  
Point Process ◽  
Stationary Point ◽  
Point Processes ◽  
Counting Process ◽  
Derived Relations ◽  
Recurrence Times ◽  
Different Types ◽  
First Recurrence ◽  
Stationary Point Processes ◽  
Event Counting

Various types of time and event sampling of a stationary and orderly bivariate point process are considered. Fundamental relations between inter-event intervals and the event counting process are derived. Relations between first forward recurrence times and their moments for different types of sampling are obtained.

Selective interaction of a Poisson and renewal process: first-order stationary point results

1970 ◽  
Vol 7 (02) ◽  
pp. 359-372 ◽  
Author(s):  
A. J. Lawrance
Keyword(s):  
Stationary Point ◽  
Joint Distribution ◽  
Point Processes ◽  
First Order ◽  
Response Interval ◽  
Selective Interaction ◽  
Counting Distribution ◽  
Stationary Point Process ◽  
Equilibrium Process ◽  
Stationary Point Processes

The simple stationarity of a previously derived equilibrium process of responses in a renewal inhibited stationary point process is established by deriving the joint distribution of the number of responses in contiguous intervals in the process. For a renewal inhibited Poisson process the variancetime function of the process is obtained; the distribution of an arbitrary between-response interval and the synchronous counting distribution are also derived following analytic justification of the required results. These results strengthen earlier results in the theory of stationary point processes. Three other point processes arising from the interaction are briefly discussed.

Some multivariate generalizations of results in univariate stationary point processes

1977 ◽  
Vol 14 (04) ◽  
pp. 748-757 ◽  
Author(s):  
Mark Berman
Keyword(s):  
Point Process ◽  
Stationary Point ◽  
Point Processes ◽  
Stationary Point Process ◽  
Stationary Point Processes

Some relationships are derived between the asynchronous and partially synchronous counting and interval processes associated with a multivariate stationary point process. A few examples are given to illustrate some of these relationships.

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