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 On the intensity of crossings by a shot noise process

1987 ◽  
Vol 19 (03) ◽  
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.

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.

On the GIX/G/∞ system

1990 ◽  
Vol 27 (3) ◽  
pp. 671-683 ◽  
Author(s):  
L. Liu ◽  
B. R. K. Kashyap ◽  
J. G. C. Templeton
Keyword(s):  
Steady State ◽  
Shot Noise ◽  
Continuous Time ◽  
Transient State ◽  
System Size ◽  
Noise Process ◽  
Shot Noise Process ◽  
Special Cases

By using a shot noise process, general results on system size in continuous time are given both in transient state and in steady state with discussion on some interesting results concerning special cases. System size before arrivals is also discussed.

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.

On the GIX/G/∞ system

1990 ◽  
Vol 27 (03) ◽  
pp. 671-683 ◽  
Author(s):  
L. Liu ◽  
B. R. K. Kashyap ◽  
J. G. C. Templeton
Keyword(s):  
Steady State ◽  
Shot Noise ◽  
Continuous Time ◽  
Transient State ◽  
System Size ◽  
Noise Process ◽  
Shot Noise Process ◽  
Special Cases

By using a shot noise process, general results on system size in continuous time are given both in transient state and in steady state with discussion on some interesting results concerning special cases. System size before arrivals is also discussed.

scholarly journals Shot noise generated by a semi-Markov process

1973 ◽  
Vol 10 (3) ◽  
pp. 685-690 ◽  
Author(s):  
Woollcott Smith
Keyword(s):  
Markov Process ◽  
Shot Noise ◽  
Noise Process ◽  
Shot Noise Process ◽  
Semi Markov Process

In this note a model for shot noise generated by a semi-Markov process is developed. The moments of the shot noise process are found, and some applications of this model are briefly indicated.

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