All Questions
9 questions
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Existence of derivative of distribution of exponential family?
Suppose $(X, \mathcal{F})$ is a measurable space and $\left\{F_\theta, \theta \in \Theta\right\}$ is a distribution family on $(X, \mathcal{F})$. When $\left\{F_\theta, \theta \in \Theta\right\}$ is ...
2
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0
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98
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Understanding simple point processes (part 2)
This is a follow up of this previous question. I'm trying to understand the following proposition from An Introduction to the Theory of Point Processes Volume I: Elementary Theory and Methods
by Daley ...
- 181
3
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94
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Understanding simple point processes
Background
I'm studying the basic theory of Random Finite Sets (RFS), which is the name that is used in my field to denote simple point processes.
A simple point process is a random variable whose ...
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2
votes
2
answers
211
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Limit of a integral whose integrand diverges under the limit
I am trying to simplify the following limit of integral where $\mu$ is given:
$$p(y) = \lim_{\sigma \to 0} \int_{\mathbb R} |x| \cdot \frac{1}{\sqrt{2\pi\sigma^2} } e^{-\frac{1}{2\sigma^2} (xy - \mu)^...
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1
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1
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Resources to understand Lebesgue measure of Brownian motion's path [closed]
[https://www.math.uchicago.edu/~may/VIGRE/VIGRE2011/REUPapers/Hansen.pdf][page 12] and [peter morters][page 47]
Let $B$ be a stanrd Brownian Motion and $R$ a function defined on $\mathbb{R}^2$ such ...
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1
answer
133
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Convoluted Cantor-like measure which has a continuous component [duplicate]
Let $\mu$ be a finite measure on $\mathbb R$ which has no atoms, and no component continuous with respect to Lebesgue measure. An example is the law of the random variable
$$
\sum_{k\ge 1}3^{-k}X_k
$$...
- 1,352
2
votes
1
answer
1k
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measure of a degenerate Gaussian distribution
I want to do computations with a degenerate Gaussian measure, but I do not know how to represent it
in a close form.
After starting with a Gaussian random variable and restricting it to a condition, I ...
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5
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2
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2k
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Tight sequence of measures
This is probably a very easy question for experts in probability or measure theory.
I have a sequence of finite measures $\mu_{n}$ on a non-compact metric space $X$ such that $\mu_{n}$ converges to $\...
- 38
1
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1
answer
149
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Convergence of measurable functions in a locally compact space
Set $(X,\mathcal{B})$ a measurable space. If $f:X\rightarrow[0,\infty)$ is a measurable function then exists a sequence of simple functions $\{s_n\}_{n\geq1}$ such that
$$0\leq s_1 \leq s_2\leq \...
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