# Questions tagged [point-processes]

This tag is for questions concerning point processes such as poisson point processes or any other point process.

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### Why is the Sine Kernel admissible as the kernel of a DPP? [closed]

The Sine DPP is given by the kernel $$K(x,y)=\frac{\sin(\pi(x-y))}{\pi(x-y)}$$ and is a well-known example of a Kernel for a determinantal point process. However, this kernel is not always positive. ...
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1 vote
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### Counterexample for Mecke equation in higher dimensions

I am currently reading the book Lectures on the Poisson Process by Gunter Last and Mathew Penrose. (The book can be found here.) I have a question about an exercise in the book's 4th chapter (Exercise ...
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### Meaning of Janossy densities

I'm studying the theory of finite point processes on "An Introduction to the Theory of Point Processes: Volume I: Elementary Theory and Methods, Second Edition" by Daley and Vere-Jones. I ...
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1 vote
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### Conditional intensity of a generalized Poisson process

Assume that we have a temporal point process on the interval [0, 1], where the number of events $N$ is distributed according to some PMF $p(N = n)$. Conditioned on $N$, the arrivals times of the ...
1 vote
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### Mean value for the number of neighbors of typical cell on a manifold

For Poisson-Voronoi tessellations of $\mathbb R^2$, the expected number of vertices on the boundary of the typical cell is 6. Proofs of this can be found in section 9.3.4 of Stochastic Geometry and ...
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### Gibbs point process

I am reading in the book Spatial Point Patterns by Baddley et al. that "all finite point process models (under reasonable conditions) can be represented mathematically as Gibbs models". I couldn't ...
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1 vote
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### Poisson process: finding probability of 1 count in an interval given that 0 counts happen in a subinterval

This was in my exam today and I'm not sure what's the correct answer. Let's say that the number of people that enter into a store in the interval $(0,t]$ (in hours) is a Poisson process where $30$ ...
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1 vote
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### Doob-Meyer decomposition with respect to different filtrations

It is known that the Doob-Meyer theorem gives us a unique decomposition, $N(t)=A(t)+M(t)$ and the compensator part may conditional on a filtration $F_1$: $A(t|F_1)$. My question is: Does the Doob-...
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### Homogenous Poisson Point Process to Binomial PPP

In my analysis, I am considering some nodes distributed as Homogenous Poisson Point Process (H-PPP) $\Phi$ with intensity $\lambda$. At a certain point during analysis, I need to focus on the ...
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