# Questions tagged [point-processes]

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

85 questions
Filter by
Sorted by
Tagged with
1 vote
32 views

### 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. ...
1 vote
22 views

### 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 ...
1 vote
18 views

159 views

### 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 ...
1 vote
42 views

### 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
27 views

### 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 ...
110 views

71 views

### 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 ...
1 vote
72 views

### 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 $30$ ...
1 vote
48 views

### 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-...
139 views

### 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 ...