Lectures on the Poisson Process

@inproceedings{Penrose2017LecturesOT,
  title={Lectures on the Poisson Process},
  author={Mathew D. Penrose},
  year={2017}
}
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260 Citations
Highly Influential Citations
34
Background Citations
88
Methods Citations
41
Results Citations
3

260 Citations

Structural properties of Gibbsian point processes in abstract spaces
In the language of random counting measures many structural properties of the Poisson process can be studied in arbitrary measurable spaces. We provide a similarly general treatise of Gibbs…
Malliavin calculus for marked binomial processes: portfolio optimisation in the trinomial model and compound Poisson approximation
In this paper we develop a stochastic analysis for marked binomial processes, that can be viewed as the discrete analogues of marked Poisson processes. The starting point is the statement of a…
Hyperuniform and rigid stable matchings
TLDR
A stable partial matching of the (possibly randomized) $d$-dimensional lattice with a stationary determinantal point process $\Psi$ on $\mathbb{R}^d$ with intensity $\alpha>1$ with hyperuniformity and number rigid properties is studied.
On almost sure convergence of random variables with finite chaos decomposition
Under mild conditions on a family of independent random variables $(X_n)$ we prove that almost sure convergence of a sequence of tetrahedral polynomial chaoses of uniformly bounded degrees in the…
Lace Expansion and Mean-Field Behavior for the Random Connection Model
TLDR
The lace expansion is adapted to fit the framework of the underlying continuum-space Poisson point process to derive the triangle condition in sufficiently high dimension and furthermore to establish the infra-red bound.
Brownian Polymers in Poissonian Environment: a survey
We consider a space-time continuous directed polymer in random environment. The path is Brownian and the medium is Poissonian. We review many results obtained in the last decade, and also we present…
Leaves on the line and in the plane
  • M. Penrose
  • Mathematics
    Electronic Journal of Probability
  • 2020
The Dead Leaves Model (DLM) provides a random tessellation of $d$-space, representing the visible portions of fallen leaves on the ground when $d=2$. For $d=1$, we establish formulae for the…
Phase transitions for the Boolean model of continuum percolation for Cox point processes
We consider the Boolean model with random radii based on Cox point processes. Under a condition of stabilization for the random environment, we establish existence and non-existence of subcritical…
Combined Degradation Process and Remaining Useful Life Improvement in an Actuator
TLDR
The proposed degradation modeling and remaining useful life prediction are applied to a double-tank level control system and it is shown that the reliability evolution of the actuator can be estimated by probabilistic approach.
Zentrale Grenzwertsätze im Random Connection Model
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References

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