Sample path large deviations for the multiplicative Poisson shot noise process with compensation

Stochastics ◽  
2020 ◽  
pp. 1-31
Author(s):  
Hui Jiang ◽  
Qingshan Yang
Keyword(s):  
Large Deviations ◽  
Shot Noise ◽  
Sample Path ◽  
Noise Process ◽  
Shot Noise Process ◽  
Poisson Shot Noise ◽  
Sample Path Large Deviations

scholarly journals Sample Path Large Deviations of Poisson Shot Noise with Heavy-Tailed Semiexponential Distributions

2011 ◽  
Vol 48 (03) ◽  
pp. 688-698 ◽  
Author(s):  
Ken R. Duffy ◽  
Giovanni Luca Torrisi
Keyword(s):  
Large Deviations ◽  
Shot Noise ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Sample Path ◽  
Rate Function ◽  
Sample Paths ◽  
Heavy Tailed ◽  
Poisson Shot Noise ◽  
Sample Path Large Deviations

It is shown that the sample paths of Poisson shot noise with heavy-tailed semiexponential distributions satisfy a large deviation principle with a rate function that is insensitive to the shot shape. This demonstrates that, on the scale of large deviations, paths to rare events do not depend on the shot shape.

scholarly journals Sample Path Large Deviations of Poisson Shot Noise with Heavy-Tailed Semiexponential Distributions

2011 ◽  
Vol 48 (3) ◽  
pp. 688-698
Author(s):  
Ken R. Duffy ◽  
Giovanni Luca Torrisi
Keyword(s):  
Large Deviations ◽  
Shot Noise ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Sample Path ◽  
Rate Function ◽  
Sample Paths ◽  
Heavy Tailed ◽  
Poisson Shot Noise ◽  
Sample Path Large Deviations

It is shown that the sample paths of Poisson shot noise with heavy-tailed semiexponential distributions satisfy a large deviation principle with a rate function that is insensitive to the shot shape. This demonstrates that, on the scale of large deviations, paths to rare events do not depend on the shot shape.

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.

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.

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.

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