scholarly journals A Poisson shot-noise process of pulses and its scaling limits

2015 ◽  
Vol 9 (4) ◽  
Author(s):  
Mine Çaglar
Keyword(s):  
Shot Noise ◽  
Scaling Limits ◽  
Noise Process ◽  
Shot Noise Process ◽  
Poisson Shot Noise

The central limit theorem for the Poisson shot-noise process

1984 ◽  
Vol 21 (02) ◽  
pp. 287-301 ◽  
Author(s):  
John A. Lane
Keyword(s):  
Shot Noise ◽  
Sufficient Conditions ◽  
Infinitely Divisible ◽  
Noise Process ◽  
Shot Noise Process ◽  
The Central Limit Theorem ◽  
Cluster Point Process ◽  
Necessary And Sufficient ◽  
Poisson Cluster ◽  
Poisson Shot Noise

The Poisson shot-noise process discussed here takes the form f:oo H(t, s)N(ds), where N(· is the counting measure of a Poisson process and the H(·, s) are independent stochastic processes. Necessary and sufficient conditions are obtained for convergence in distribution, as t ∼ OC, to any infinitely divisible distribution. The main interest is in the explosive transient one-sided shot-noise, Y(t) = f:1 H(t, s)N(ds) where Var Y(t)∼ oc, Here conditions for asymptotic normality are discussed in detail. Important examples include the Poisson cluster point process and the integrated stationary shotnoise.

The central limit theorem for the Poisson shot-noise process

1984 ◽  
Vol 21 (2) ◽  
pp. 287-301 ◽  
Author(s):  
John A. Lane
Keyword(s):  
Shot Noise ◽  
Sufficient Conditions ◽  
Infinitely Divisible ◽  
Noise Process ◽  
Shot Noise Process ◽  
The Central Limit Theorem ◽  
Cluster Point Process ◽  
Necessary And Sufficient ◽  
Poisson Cluster ◽  
Poisson Shot Noise

The Poisson shot-noise process discussed here takes the form f:oo H(t, s)N(ds), where N(· is the counting measure of a Poisson process and the H(·, s) are independent stochastic processes. Necessary and sufficient conditions are obtained for convergence in distribution, as t ∼ OC, to any infinitely divisible distribution. The main interest is in the explosive transient one-sided shot-noise, Y(t) = f:1 H(t, s)N(ds) where Var Y(t)∼ oc, Here conditions for asymptotic normality are discussed in detail. Important examples include the Poisson cluster point process and the integrated stationary shotnoise.

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.

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.

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