Further results for Gauss-Poisson processes

1972 ◽  
Vol 4 (01) ◽  
pp. 151-176 ◽  
Author(s):  
R. K. Milne ◽  
M. Westcott
Keyword(s):  
Point Processes ◽  
Sufficient Conditions ◽  
Infinite Divisibility ◽  
Poisson Processes ◽  
Generating Functional ◽  
Basic Approach ◽  
New Class ◽  
Two Measures ◽  
Necessary And Sufficient ◽  
Statistical Results

Newman (1970) introduced an interesting new class of point processes which he called Gauss-Poisson. They are characterized, in the most general case, by two measures. We determine necessary and sufficient conditions on these measures for the resulting point process to be well defined, and proceed to a systematic study of its properties. These include stationarity, ergodicity, and infinite divisibility. We mention connections with other classes of point processes and some statistical results. Our basic approach is through the probability generating functional of the process.

Further results for Gauss-Poisson processes

1972 ◽  
Vol 4 (1) ◽  
pp. 151-176 ◽  
Author(s):  
R. K. Milne ◽  
M. Westcott
Keyword(s):  
Point Processes ◽  
Sufficient Conditions ◽  
Infinite Divisibility ◽  
Poisson Processes ◽  
Generating Functional ◽  
Basic Approach ◽  
New Class ◽  
Two Measures ◽  
Necessary And Sufficient ◽  
Statistical Results

Newman (1970) introduced an interesting new class of point processes which he called Gauss-Poisson. They are characterized, in the most general case, by two measures. We determine necessary and sufficient conditions on these measures for the resulting point process to be well defined, and proceed to a systematic study of its properties. These include stationarity, ergodicity, and infinite divisibility. We mention connections with other classes of point processes and some statistical results. Our basic approach is through the probability generating functional of the process.

A note on exceedances and rare events of non-stationary sequences

1993 ◽  
Vol 30 (04) ◽  
pp. 877-888 ◽  
Author(s):  
J. Hüsler
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Rare Events ◽  
Sufficient Conditions ◽  
Stationary Sequence ◽  
Poisson Processes ◽  
Regularity Conditions ◽  
Mixing Conditions ◽  
Necessary And Sufficient ◽  
Point Process Of Exceedances

Exceedances of a non-stationary sequence above a boundary define certain point processes, which converge in distribution under mild mixing conditions to Poisson processes. We investigate necessary and sufficient conditions for the convergence of the point process of exceedances, the point process of upcrossings and the point process of clusters of exceedances. Smooth regularity conditions, as smooth oscillation of the non-stationary sequence, imply that these point processes converge to the same Poisson process. Since exceedances are asymptotically rare, the results are extended to triangular arrays of rare events.

High-Level exceedances of regenerative and semi-stationary processes

1980 ◽  
Vol 17 (02) ◽  
pp. 423-431 ◽  
Author(s):  
Richard Serfozo
Keyword(s):  
Point Processes ◽  
Stationary Process ◽  
Sufficient Conditions ◽  
Poisson Processes ◽  
Partial Sums ◽  
Stationary Processes ◽  
Special Cases ◽  
Cumulative Amount ◽  
High Level ◽  
Necessary And Sufficient

The cumulative amount of time that a regenerative or semi-stationary process exceeds a high level and other measures of these exceedances are considered as special cases of a non-decreasing stochastic process of partial sums. We present necessary and sufficient conditions for these exceedance processes to converge in distribution to Poisson processes or processes with stationary independent non-negative increments as the level goes to infinity. We apply our results to random walks, M/M/s queues, and thinnings of point processes.

High-Level exceedances of regenerative and semi-stationary processes

1980 ◽  
Vol 17 (2) ◽  
pp. 423-431 ◽  
Author(s):  
Richard Serfozo
Keyword(s):  
Point Processes ◽  
Stationary Process ◽  
Sufficient Conditions ◽  
Poisson Processes ◽  
Partial Sums ◽  
Stationary Processes ◽  
Special Cases ◽  
Cumulative Amount ◽  
High Level ◽  
Necessary And Sufficient

The cumulative amount of time that a regenerative or semi-stationary process exceeds a high level and other measures of these exceedances are considered as special cases of a non-decreasing stochastic process of partial sums. We present necessary and sufficient conditions for these exceedance processes to converge in distribution to Poisson processes or processes with stationary independent non-negative increments as the level goes to infinity. We apply our results to random walks, M/M/s queues, and thinnings of point processes.

A note on exceedances and rare events of non-stationary sequences

1993 ◽  
Vol 30 (4) ◽  
pp. 877-888 ◽  
Author(s):  
J. Hüsler
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Rare Events ◽  
Sufficient Conditions ◽  
Stationary Sequence ◽  
Poisson Processes ◽  
Regularity Conditions ◽  
Mixing Conditions ◽  
Necessary And Sufficient ◽  
Point Process Of Exceedances

Exceedances of a non-stationary sequence above a boundary define certain point processes, which converge in distribution under mild mixing conditions to Poisson processes. We investigate necessary and sufficient conditions for the convergence of the point process of exceedances, the point process of upcrossings and the point process of clusters of exceedances. Smooth regularity conditions, as smooth oscillation of the non-stationary sequence, imply that these point processes converge to the same Poisson process. Since exceedances are asymptotically rare, the results are extended to triangular arrays of rare events.

Twisted Sasakian Metric on the Tangent Bundle and Harmonicity

2021 ◽  
Vol 62 ◽  
pp. 53-66
Author(s):  
Fethi Latti ◽  
◽  
Hichem Elhendi ◽  
Lakehal Belarbi
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Tangent Bundle ◽  
Vector Fields ◽  
Sufficient Conditions ◽  
Harmonic Vector ◽  
New Class ◽  
Necessary And Sufficient ◽  
Sasakian Metric ◽  
Harmonic Vector Fields

In the present paper, we introduce a new class of natural metrics on the tangent bundle $TM$ of the Riemannian manifold $(M,g)$ denoted by $G^{f,h}$ which is named a twisted Sasakian metric. A necessary and sufficient conditions under which a vector field is harmonic with respect to the twisted Sasakian metric are established. Some examples of harmonic vector fields are presented as well.

scholarly journals On a topology between Tα and Tγα

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3209-3221
Author(s):  
Dimitrije Andrijevic
Keyword(s):  
Topological Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Closure Operators ◽  
New Class ◽  
Necessary And Sufficient

Using the topology T in a topological space (X,T), a new class of generalized open sets called ?-preopen sets, is introduced and studied. This class generates a new topology Tg which is larger than T? and smaller than T??. By means of the corresponding interior and closure operators, among other results, necessary and sufficient conditions are given for Tg to coincide with T? , T? or T??.

Order statistics, Poisson processes and repairable systems

1976 ◽  
Vol 13 (03) ◽  
pp. 519-529 ◽  
Author(s):  
Douglas R. Miller
Keyword(s):  
Order Statistics ◽  
Point Processes ◽  
Failure Time ◽  
Sufficient Conditions ◽  
Renewal Processes ◽  
Repairable Systems ◽  
Homogeneous Poisson Process ◽  
Necessary And Sufficient ◽  
Non Homogeneous Poisson Process ◽  
Weibull Process

Necessary and sufficient conditions are presented under which the point processes equivalent to order statistics of n i.i.d. random variables or superpositions of n i.i.d. renewal processes converge to a non-degenerate limiting process as n approaches infinity. The limiting process must be one of three types of non-homogeneous Poisson process, one of which is the Weibull process. These point processes occur as failure-time models in the reliability theory of repairable systems.

Max-infinite divisibility

1977 ◽  
Vol 14 (02) ◽  
pp. 309-319 ◽  
Author(s):  
A. A. Balkema ◽  
S. I. Resnick
Keyword(s):  
Distribution Function ◽  
Sufficient Conditions ◽  
Infinite Divisibility ◽  
Necessary And Sufficient Conditions ◽  
Infinitely Divisible ◽  
Extremal Processes ◽  
Necessary And Sufficient

Necessary and sufficient conditions are given for a distribution function in ℝ2 to be max-infinitely divisible. The d.f. F is max i.d. if F t is a d.f. for every t > 0. This property is essential in defining multivariate extremal processes and arises in an approach to the study of the range of an i.i.d. sample.

scholarly journals Positivity and stabilization of fractional 2D linear systems described by the Roesser model

2010 ◽  
Vol 20 (1) ◽  
pp. 85-92 ◽  
Author(s):  
Tadeusz Kaczorek ◽  
Krzysztof Rogowski
Keyword(s):  
Linear Systems ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Roesser Model ◽  
Fractional Difference ◽  
Fractional Systems ◽  
New Class ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems

Positivity and stabilization of fractional 2D linear systems described by the Roesser modelA new class of fractional 2D linear discrete-time systems is introduced. The fractional difference definition is applied to each dimension of a 2D Roesser model. Solutions of these systems are derived using a 2DZ-transform. The classical Cayley-Hamilton theorem is extended to 2D fractional systems described by the Roesser model. Necessary and sufficient conditions for the positivity and stabilization by the state-feedback of fractional 2D linear systems are established. A procedure for the computation of a gain matrix is proposed and illustrated by a numerical example.

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