Concept

Campbell's theorem (probability)

Related publications (32)

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 ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

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 ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

Low-dimensional firing-rate dynamics for populations of renewal-type spiking neurons

Tilo Schwalger

The macroscopic dynamics of large populations of neurons can be mathematically analyzed using low-dimensional firing-rate or neural-mass models. However, these models fail to capture spike synchronization effects and nonstationary responses of the populati ...

AMER PHYSICAL SOC2020

Causal inference in continuous time: an example on prostate cancer therapy

Mats Julius Stensrud, Pal Christie Ryalen

In marginal structural models (MSMs), time is traditionally treated as a discrete parameter. In survival analysis on the other hand, we study processes that develop in continuous time. Therefore, Røysland (2011. A martingale approach to continuous-time mar ...

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

Stochastic partial differential equations driven by Lévy white noises

Thomas Marie Jean-Baptiste Humeau

We study various aspects of stochastic partial differential equations driven by Lévy white noise. This driving noise, which is a generalization of Gaussian white noise, can be viewed either as a generalized random process or as an independently scattered r ...

EPFL2017

Gaussian versus Sparse Stochastic Processes

Julien René Pierre Fageot

Although our work lies in the field of random processes, this thesis was originally motivated by signal processing applications, mainly the stochastic modeling of sparse signals. We develop a mathematical study of the innovation model, under which a signal ...

EPFL2017

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

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