Publications associées à Campbell's theorem (probability)

Generating Sparse Stochastic Processes Using Matched Splines

Michaël Unser, Leello Tadesse Dadi, Shayan Aziznejad

We provide an algorithm to generate trajectories of sparse stochastic processes that are solutions of linear ordinary differential equations driven by Levy white noises. A recent paper showed that these processes are limits in law of generalized compound-P ...

2020

Gaussian and sparse processes are limits of generalized Poisson processes

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann

The theory of sparse stochastic processes offers a broad class of statistical models to study signals, far beyond the more classical class of Gaussian processes. In this framework, signals are represented as realizations of random processes that are soluti ...

2020

On Jump-Diffusive Driving Noise Sources: Some Explicit Results and Applications

Max-Olivier Hongler, Roger Filliger

We study some linear and nonlinear shot noise models where the jumps are drawn from a compound Poisson process with jump sizes following an Erlang-m distribution. We show that the associated Master equation can be written as a spatial mth order partial dif ...

Springer2019

Interference Functionals in Poisson Networks

Martin Haenggi

We propose and prove a theorem that allows the calculation of a class of functionals on Poisson point processes that have the form of expected values of sum-products of functions. In proving the theorem, we present a variant of the Campbell-Mecke theorem f ...

Ieee-Inst Electrical Electronics Engineers Inc2016

Interpretation of Continuous-Time Autoregressive Processes as Random Exponential Splines

Michaël Unser, Julien René Pierre Fageot, John Paul Ward

We consider the class of continuous-time autoregressive (CAR) processes driven by (possibly non-Gaussian) Lévy white noises. When the excitation is an impulsive noise, also known as compound Poisson noise, the associated CAR process is a random non-uniform ...

IEEE2015

Max-stable processes and stationary systems of Levy particles

Sebastian Engelke

We study stationary max-stable processes {n(t): t is an element of R} admitting a representation of the form n(t) = max(i is an element of N) (U-i +Y-i(t)), where Sigma(infinity)(i=1) delta U-i is a Poisson point process on R with intensity e(-u)du, and Y1 ...

Elsevier2015

Invariant manifolds with boundary for jump-diffusions

Damir Filipovic

We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds with boundary in Hilbert spaces for stochastic partial differential equations driven by Wiener processes and Poisson random measures. ...

Univ Washington, Dept Mathematics2014

Secure Wireless Communications via Cooperative Transmitting

Ninoslav Marina

Information-theoretic secrecy is combined with cryptographic secrecy to create a secret-key exchange protocol for wireless networks. A network of transmitters, which already have cryptographically secured channels between them, cooperate to exchange a secr ...

Hindawi Publishing Corporation2014

3D Poisson Microscopy Deconvolution With Hessian Schatten-Norm Regularization

Michaël Unser, Stamatios Lefkimmiatis

Inverse problems with shot noise arise in many modern biomedical imaging applications. The main challenge is to obtain an estimate of the underlying specimen from measurements corrupted by Poisson noise. In this work, we propose an efficient framework for ...

IEEE2013

Stochastic dynamics of snow avalanche occurrence by superposition of Poisson processes

Paolo Perona, Benoît Crouzy

We study the dynamics of systems with deterministic trajectories randomly forced by instantaneous discontinuous jumps occurring according to two different compound Poisson processes. One process, with constant frequency, causes instantaneous positive rando ...

Royal Soc2012