Question

Let ${Y_t}$ be a stationary process with mean zero and let $a$ and $b$ be constants. Prove $X_t$ is a stationary

score 212 · Answer 1 · 2023-10-24 02:11:57

212

Views

Let ${Y_t}$ be a stationary process with mean zero and let $a$ and $b$ be constants. Prove $X_t$ is a stationary

Published on 24 Oct 2023 - 2:11

score 39 · Answer 2 · 2023-11-02 00:03:58

39

Views

Doubt related to weakly stationary stochastic processes.

Published on 02 Nov 2023 - 0:03

score 73 · Answer 3 · 2023-11-02 09:18:50

73

Views

Proving $S_m=\sum\limits_{j=1}^m{\theta^j X_{n-j}}$ converges in mean square as $m\to \infty$

Published on 02 Nov 2023 - 9:18

score 174 · Answer 4 · 2026-03-26 06:33:33

174

Views

Is an AR(1) process with Bernoulli errors mixing or ergodic?

Published on 26 Mar 2026 - 6:33

score 18 · Answer 5 · 2023-11-11 22:56:04

18

Views

Finding the spectral measure of a of a weakly stationary process

Published on 11 Nov 2023 - 22:56

score 25 · Answer 6 · 2023-11-15 07:36:53

25

Views

Are transition probabilities always absolutely continuous w.r.t. invariant measure?

Published on 15 Nov 2023 - 7:36

score 38 · Answer 7 · 2026-02-23 04:57:47

38

Views

Expression of the stationary distribution of a Markov Chain (PageRank)

Published on 23 Feb 2026 - 4:57

score 55 · Answer 8 · 2026-03-25 18:55:37

55

Views

Can anyone help to solve this task ?In a multiple-choice test with m options, a student knows the correct answer with probability p,...?

Published on 25 Mar 2026 - 18:55

score 58 · Answer 9 · 2023-12-21 16:19:55

58

Views

$\beta$-mixing in Asmptotically Stochasitic (Random) Process

Published on 21 Dec 2023 - 16:19

score 38 · Answer 10 · 2024-01-01 22:51:41

38

Views

Stationary Ornstein-Uhlenbeck process - Brownian motion for $t<0$?

Published on 01 Jan 2024 - 22:51

score 62 · Answer 11 · 2024-01-02 09:59:23

62

Views

Example of a Markov Chain which is stationary but not reversible

Published on 02 Jan 2024 - 9:59

score 46 · Answer 12 · 2024-01-04 19:08:26

46

Views

Stationary distribution for a function of Markov process

Published on 04 Jan 2024 - 19:08

score 22 · Answer 13 · 2024-01-06 18:38:33

22

Views

Conditional mean of an ARMA($p,q$) process

Published on 06 Jan 2024 - 18:38

score 40 · Answer 14 · 2024-01-19 17:42:42

40

Views

If $\{X_{t}:t\in\mathbb{Z}\}$ is strictly stationary, then $Y_{t}:=g(X_{t},\dots, X_{t+m-1})$ is also strictly stationary.

Published on 19 Jan 2024 - 17:42

score 80 · Answer 15 · 2024-01-21 17:16:16

80

Views

Show that $X_{t}:=\alpha X_{t-1}+\epsilon_{t}$ is strictly stationary for $|\alpha|<1$ and $\epsilon_{t}$ i.i.d$~\sim N(0,\sigma^{2})$.

Published on 21 Jan 2024 - 17:16

List Question

Let ${Y_t}$ be a stationary process with mean zero and let $a$ and $b$ be constants. Prove $X_t$ is a stationary

Doubt related to weakly stationary stochastic processes.

Proving $S_m=\sum\limits_{j=1}^m{\theta^j X_{n-j}}$ converges in mean square as $m\to \infty$

Is an AR(1) process with Bernoulli errors mixing or ergodic?

Finding the spectral measure of a of a weakly stationary process

Are transition probabilities always absolutely continuous w.r.t. invariant measure?

Expression of the stationary distribution of a Markov Chain (PageRank)

Can anyone help to solve this task ?In a multiple-choice test with m options, a student knows the correct answer with probability p,...?

$\beta$-mixing in Asmptotically Stochasitic (Random) Process

Stationary Ornstein-Uhlenbeck process - Brownian motion for $t<0$?

Example of a Markov Chain which is stationary but not reversible

Stationary distribution for a function of Markov process

Conditional mean of an ARMA($p,q$) process

If $\{X_{t}:t\in\mathbb{Z}\}$ is strictly stationary, then $Y_{t}:=g(X_{t},\dots, X_{t+m-1})$ is also strictly stationary.

Show that $X_{t}:=\alpha X_{t-1}+\epsilon_{t}$ is strictly stationary for $|\alpha|<1$ and $\epsilon_{t}$ i.i.d$~\sim N(0,\sigma^{2})$.

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