All Questions
Tagged with geometric-probability stochastic-processes
11
questions
7
votes
0
answers
189
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Definition of Random Measures
Introducing the notion of a random measure, textbooks usually start with a locally compact second countable Hausdorff space. Where does this requirement come from?
I would like to have a motivation ...
- 161
0
votes
1
answer
2k
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Branching Process - Extinction probability geometric
Consider a branching process with offspring distribution Geometric($\alpha$); that is,
$p_{k} =α(1−α)^k$ for $k≥0$.
a) For what values of $α ∈ (0, 1)$ is the extinction probability $q = 1$.
b) Use ...
9
votes
2
answers
2k
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Given a knight on an infinite chess board that moves randomly, what's the expected number of distinct squares it reaches in 50 moves?
I was asked this in an interview and wasn't sure how to frame the answer. Basically as in the question you have a knight on an infinite chess board and it chooses one of its valid 8 moves uniformly at ...
- 138
4
votes
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245
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Hands-On Matlab Resources for Wireless Networks Modeling using Stochastic Geometry
Stochastic Geometry has become a very strong mathematical tool for studying and understanding several aspects of wireless communication and networks. As I write this, I find quite a large number of ...
- 429
0
votes
2
answers
202
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Distribution of Queue Length at Next Arrival
I'm trying to figure out the following:
Suppose that an $M/M/1$ is at stationarity (arrival rate $\lambda$, service rate $\mu$).
Suppose that $B$ is the next person to arrive in the queue.
What is ...
user263626
5
votes
1
answer
316
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Rain droplets falling on a line
Suppose there is a line of length $L$ cm. And it begins to rain at a constant rate of one droplet per second. Once a drop strike the line and it wets 1 cm of the line. What is the expected number of ...
- 651
3
votes
0
answers
57
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Hitting time for a random walk with non constant steps
Consider the sequence of random variables defined by $X_0= 0$ and $X_{i+1} = X_i + U_i$, where $U_i$ are iid with uniform law on the ball of radius $\varepsilon$ (in dimension $d$). Define $T = \min\{...
- 618
1
vote
1
answer
758
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Calculate the probability with respect to Brownian motion.
Given two positive constants $a,b>0$. Suppose both $B_1$ and $B_2$ are 2D standard complex Brownian motions which start from $0$. Let $T_a=\inf\{t>0:|B_1|=a\}$,$T_b=\inf\{t>0:|B_2|=b\}$. ...
- 45
1
vote
1
answer
137
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Concluding from limiting behavior
I've recently seen the following question on the internet:
If I wanted to randomly find someone in an amusement park, would my odds of finding them be greater if I stood still or roamed around?
...
- 273
3
votes
1
answer
250
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Motivation and application for stochastic geometry.
I am starting a PhD, and there is a good chance that my project will be oriented in the study of random polytopes or/and random mosaics. I was wondering what are the motivations and applications of ...
- 2,083
5
votes
3
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Distribution of shapes of Delaunay triangles
Does anyone know the probability distribution of the shapes of Delaunay triangles in a constant-intensity Poisson process in the plane?
Slightly later edit: One can imagine performing the experiment ...
