Inequalities for the M/G/∞ queue and related shot noise processes

1987 ◽  
Vol 24 (4) ◽  
pp. 978-989 ◽  
Author(s):  
Fred W. Huffer
Keyword(s):  
Poisson Process ◽  
Shot Noise ◽  
Convex Functions ◽  
Sample Path ◽  
Noise Process ◽  
Shot Noise Process

Suppose that pulses arrive according to a Poisson process of rate λ with the duration of each pulse independently chosen from a distribution F having finite mean. Let X(t) be the shot noise process formed by the superposition of these pulses. We consider functionals H(X) of the sample path of X(t). H is said to be L-superadditive if for all functions f and g. For any distribution F for the pulse durations, we define H(F) = EH(X). We prove that if H is L-superadditive and for all convex functions ϕ, then . Various consequences of this result are explored.

Inequalities for the M/G/∞ queue and related shot noise processes

1987 ◽  
Vol 24 (04) ◽  
pp. 978-989 ◽  
Author(s):  
Fred W. Huffer
Keyword(s):  
Poisson Process ◽  
Shot Noise ◽  
Convex Functions ◽  
Sample Path ◽  
Noise Process ◽  
Shot Noise Process

Suppose that pulses arrive according to a Poisson process of rate λ with the duration of each pulse independently chosen from a distribution F having finite mean. Let X(t) be the shot noise process formed by the superposition of these pulses. We consider functionals H(X) of the sample path of X(t). H is said to be L-superadditive if for all functions f and g. For any distribution F for the pulse durations, we define H(F) = EH(X). We prove that if H is L-superadditive and for all convex functions ϕ, then . Various consequences of this result are explored.

High density shot noise and gaussianity

1971 ◽  
Vol 8 (1) ◽  
pp. 118-127 ◽  
Author(s):  
A. Papoulis
Keyword(s):  
Distribution Function ◽  
Poisson Process ◽  
Shot Noise ◽  
Average Density ◽  
Normal Process ◽  
Noise Process ◽  
Shot Noise Process ◽  
Mean And Variance ◽  
Image Position ◽  
Random Times

The distance from Gaussianity of the shot noise process is considered, where ti are the random times of a Poisson process with average density λ(t). With F(x) the distribution function of x(t) and G(x) that of a normal process with the same mean and variance as x(t) it is shown that where If the process x(t) is stationary with λ(t) =λ and h(t, τ) = h(t – τ) and the function h(t) is bandlimited by ωc, then the above yields

Prediction of shot noise

1999 ◽  
Vol 36 (2) ◽  
pp. 374-388 ◽  
Author(s):  
Robert B. Lund ◽  
Ronald W. Butler ◽  
Robert L. Paige
Keyword(s):  
Poisson Process ◽  
Shot Noise ◽  
Saddlepoint Approximation ◽  
Conditional Distributions ◽  
Conditional Mean ◽  
Noise Process ◽  
Shot Noise Process ◽  
Independent And Identically Distributed

Prediction of future values of a shot noise process observed on a discrete lattice of points is considered. The shot magnitudes are assumed to be independent and identically distributed and to arrive via a Poisson process; the effect of each shot dissipates and/or accumulates according to a known shot function. Conditional mean and linear point predictors of future process values are developed. Distributional prediction, obtained through saddlepoint approximation of the conditional distributions of the process, is also explored.

Prediction of shot noise

1999 ◽  
Vol 36 (02) ◽  
pp. 374-388 ◽  
Author(s):  
Robert B. Lund ◽  
Ronald W. Butler ◽  
Robert L. Paige
Keyword(s):  
Poisson Process ◽  
Shot Noise ◽  
Saddlepoint Approximation ◽  
Conditional Distributions ◽  
Conditional Mean ◽  
Noise Process ◽  
Shot Noise Process ◽  
Independent And Identically Distributed

Prediction of future values of a shot noise process observed on a discrete lattice of points is considered. The shot magnitudes are assumed to be independent and identically distributed and to arrive via a Poisson process; the effect of each shot dissipates and/or accumulates according to a known shot function. Conditional mean and linear point predictors of future process values are developed. Distributional prediction, obtained through saddlepoint approximation of the conditional distributions of the process, is also explored.

High density shot noise and gaussianity

1971 ◽  
Vol 8 (01) ◽  
pp. 118-127 ◽  
Author(s):  
A. Papoulis
Keyword(s):  
Distribution Function ◽  
Poisson Process ◽  
Shot Noise ◽  
Average Density ◽  
Normal Process ◽  
Noise Process ◽  
Shot Noise Process ◽  
Mean And Variance ◽  
Image Position ◽  
Random Times

The distance from Gaussianity of the shot noise processis considered, wheretiare the random times of a Poisson process with average densityλ(t).WithF(x) the distribution function ofx(t) andG(x) that of a normal process with the same mean and variance asx(t) it is shown thatwhereIf the processx(t) is stationary with λ(t) =λandh(t, τ) =h(t – τ) and the functionh(t) is bandlimited by ωc, then the above yields

scholarly journals On the intensity of crossings by a shot noise process

1987 ◽  
Vol 19 (3) ◽  
pp. 743-745 ◽  
Author(s):  
Tailen Hsing
Keyword(s):  
Shot Noise ◽  
Marginal Probability ◽  
Noise Process ◽  
Shot Noise Process

The crossing intensity of a level by a shot noise process with a monotone response is studied, and it is shown that the intensity can be naturally expressed in terms of a marginal probability.

scholarly journals A Renewal Shot Noise Process with Subexponential Shot Marks

Risks ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 63
Author(s):  
Yiqing Chen
Keyword(s):  
Asymptotic Formula ◽  
Shot Noise ◽  
Crucial Role ◽  
Random Variables ◽  
Tail Probability ◽  
Noise Process ◽  
Shot Noise Process ◽  
Precise Asymptotic

We investigate a shot noise process with subexponential shot marks occurring at renewal epochs. Our main result is a precise asymptotic formula for its tail probability. In doing so, some recent results regarding sums of randomly weighted subexponential random variables play a crucial role.

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