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Results tagged with pr.probability
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user 42412
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
3
votes
1
answer
203
views
Interpretation of an asymptotic result in probability
A result in asymptotic theory says the following: Let $Y$ be a real random variable with full support and $E(|Y|)<\infty$. Assume that:
$$
(A)\quad \lim_{y\rightarrow \infty} \frac{\Pr(Y\geq y)}{\Pr(Y …
- 108
1
vote
2
answers
496
views
Show convergence result
Consider the following sets:
$$
A = \Big\{ x\in X: \Pr\bigg(\lim_{n \to \infty}d\big(p_n, [\ell(x), u(x) ] \big)= 0\bigg)=1 \Big\},
$$
and
$$
A_n = \Big\{ x\in X: d\big(p_n, [\ell(x), u(x) ] \big …
- 108
2
votes
1
answer
193
views
Bound the probability that a point belongs to a set
Let $(a_k)_{k \geq 1}$ be random variables taking values on a finite subset $B$. Assume that
$$
(1) \quad \Pr\Big (\lim_{n\rightarrow +\infty}d(\frac{1}{n}\sum_{k=1}^n 1_{[a_k = b]}, [v_\ell(b,\theta_ …
- 108
0
votes
1
answer
171
views
Bound the expectation of an average
Let $(a_n)_{n \geq 1}$ be random variables taking values on a finite subset $B$. Assume that $\nu_l(b) \le P[a_n = b\mid a_1,\ldots,a_{n-1}] \le \nu_u(b)$ almost surely for every $n \ge 1$ and $b \in …
- 108
3
votes
1
answer
381
views
A convergence problem
I have a math/stat problem where I need to show the convergence of the average of a sequence of experiments to an interval. The sequence of experiments is not i.i.d., hence the standard law of large n …
- 108
2
votes
1
answer
375
views
Extension of subcopulas to copulas
This question is about the extension of subcopulas to copulas, shown in Sklar, A. (1996), "Random variables, distribution functions, and copulas: A personal look backward and forward." Institute of M …
- 108
2
votes
1
answer
88
views
Probability measure of trapezoidal area [closed]
Let $Pr_{(X,Y)}$ be a probability distribution of a random vector $(X,Y)$. Let $F$ be the cumulative distribution function of $(X,Y)$. Define
$$
\mathcal{A}\equiv \{(x,y): x\leq 2 \text{ and }x-y\leq …
- 108
1
vote
1
answer
179
views
From probability distribution in $\mathbb{R}^3$ to probability distribution in $\mathbb{R}^4$
I am working on a research paper where I need to investigate conditions for the existence of probability distributions satisfying certain characteristics. I have already asked a related question (here …
- 108
0
votes
2
answers
333
views
Conditions for existence of a distribution with full support
Consider a $6\times 1$ continuous random vector
$$
\eta\equiv (\eta_1,\eta_2,..., \eta_6)
$$
satisfying the following property:
$$
\underbrace{\begin{pmatrix}
\eta_1\\
\eta_2\\
\eta_3
\end{pmatrix}}_{ …
- 108
2
votes
1
answer
256
views
About a mixture
Consider the following mixture model for a univariate density function
$$
(1) \quad f(x)=\int_{(m, \sigma^2)\in D} g(x; m, \sigma^2) \mu(d(m, \sigma^2))
$$
where $D$ is a compact subset of $\mathbb{R} …
- 108