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Crossings of smooth Shot Noise Processes
| Content Provider | Hyper Articles en Ligne (HAL) |
|---|---|
| Author | Biermé, Hermine Desolneux, Agnès |
| Copyright Year | 2012 |
| Abstract | In this paper, we consider smooth shot noise processes and their expected number of level crossings. When the kernel response function is sufficiently smooth, the mean number of crossings function is obtained through an integral formula. Moreover, as the intensity increases, or equivalently as the number of shots becomes larger, a normal convergence to the classical Rice's formula for Gaussian processes is obtained. The Gaussian kernel function, that corresponds to many applications in Physics, is studied in detail and two different regimes are exhibited. |
| Related Links | https://hal.science/hal-00589560/file/SmoothShotpreprint.pdf |
| ISSN | 10505164 |
| Issue Number | 6 |
| Volume Number | 22 |
| Journal | The Annals of Applied Probability |
| e-ISSN | 21688737 |
| Language | English |
| Publisher | HAL CCSD Institute of Mathematical Statistics (IMS) |
| Publisher Date | 2012-12-01 |
| Access Restriction | Open |
| Subject Keyword | Shot noise Characteristic function Infinitely divisible process Poisson process Crossings Stationary process |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics Statistics, Probability and Uncertainty Statistics and Probability |
