All Questions
Tagged with sum convergence
6
questions
4
votes
1
answer
63
views
Convergence of an infinite sum of weighted independent and identically distributed random variable
Let $z_i$ be $i.i.d$ random variable with $E(z_i)=0$ and $E(Z_i^2)=1$ with a symmetric distribution. Further, $|\beta|<1$.
Now consider $\sum\limits_{i=1}^{\infty} \beta^i (z_i+|z_i|)$. I want to ...
- 53
2
votes
0
answers
52
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Numerical evaluation of infinite sums
I am working with Skellam random variables and I would like to evaluate the CDF of the absolute value of a Skellam random variable in which both Poisson random variables have the same rate, $\lambda_1 ...
- 530
2
votes
1
answer
143
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How to prove absolute summabilities implies the absolute summability of the product series?
In SHUMWAY 2017 Time Series Analysis and Its Applications with R examples 4E, page 486, it states:
$\Sigma_{j=-\infty}^{\infty} |a_j| < \infty$ and $\Sigma_{j=-\infty}^{\infty} |b_j| < \infty$ ...
- 549
2
votes
1
answer
547
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Why does absolutely-summable weights ensures a linear series itself summable (convergent)? Some questions on def'n of Linear Series
A "linear series" $y_t$ is the linear combination $$y_t - \mu = \sum_{i=-\infty}^{\infty}\psi_iL^i\nu_t = \sum_{i=-\infty}^{\infty}\psi_i\nu_{t-i}=S(L)\nu_t $$
of weighted (by $\psi_i$ weights) lags ...
- 549
2
votes
1
answer
1k
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Understanding the infinite sum of random variables
I am doing a course on time series analysis, and am struggling with this definition:
We call a weakly stationary process $\{X_t\}$ invertible with respect to a
white noise $\{\epsilon_t\}$ if ...
- 175
3
votes
1
answer
290
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Can we show this sum of Gamma CDF converges, and if so can we derive its limit?
This is a bit of a strange question, but suppose I have some random variables.
$$Y_i \sim Gamma(i,\lambda)$$
Where this comes from the fact that each $Y_i$ is defined as the sum of $i$ independent ...
- 1,779