Tagged Questions
0
votes
1answer
53 views
correlation between two different variables
I am studying stochastic processes and found the next problem:
Let $A$ and $\Phi $ be two independent random variables such that $E(A) = 0$, $E(A^2) < \infty$, and $\Phi$ is uniformly distributed ...
3
votes
1answer
78 views
Autocorrelation of wrapped Wiener process
Let $\phi(t)$ be a Brownian Walk (Wiener Process), where $\phi\in[0,2\pi)$. As such we work with the variable $z(t)=e^{i\phi(t)}$. I would like to calculate
$$E(z(t)z(t+\tau)).$$
This is equal to ...
1
vote
1answer
46 views
How can I show that $z_i =\cos(iw)$ where $w$ is uniform on $[0,2\pi]$ is a white noise process?
How can I show that $z_i =\cos(iw)$, where $w$ is uniform on $[0,2\pi]$ is a white noise process?
So far, I have shown $E(z_i)=0$ by integrating. However, I need to show ...
2
votes
0answers
103 views
Correlated diffusion processes and covariance matrix
I'm really noob in maths topics so I hope you will excuse me if I use terms which aren't correct.
I would like to simulate $n$ dimensional diffusion processes with $n$ noises.
Each process has its ...
1
vote
0answers
89 views
Windowed Linear Correlation
$\DeclareMathOperator \Cov {Cov}$
$\DeclareMathOperator \Var {Var}$
$\DeclareMathOperator \E {E}$
Consider the following experiment:
For $N\geq1$, consider $N$ black balls. Let us paint each black ...
0
votes
0answers
206 views
jointly stationary random process
If two wide-sense stationary processes $X(t)$ and $Y(t)$ are uncorrelated, then the cross correlation is
$R_{XY}(t_1,t_2) = E\{X(t_1)Y(t_2)\} = E\{X(t_1)\}E\{Y(t_2)\}$,
which will be a constant, ...
1
vote
1answer
50 views
constructing “pseudonoise” sequences other than (2^n)-1? (low cyclical autocorrelation)
Pseudonoise LFSR sequences of length $N = 2^k-1$ have the nice property that their cyclical autocorrelation is $N$ when the sequence is lined up with itself, and $-1$ elsewhere.
Is there a way to ...
0
votes
0answers
554 views
Pseudo-random binary sequence generated by shift register
Binary sequence generated by shift register with feedback have periodic properties. A simple 4-bit shift register shown in Fig (a). For the initial condition shown, it can be verified that the ...
4
votes
1answer
89 views
Correlations between neighboring Voronoi cells
For a sequence $X_1,X_2,X_3,\ldots$ of random variables, what it means to say $X_1$ is correlated with $X_2$ is unambiguous. It may be that the bigger $X_1$ is, the bigger $X_2$ is likely to be. If, ...
2
votes
1answer
141 views
example on variance of stochastic processes
I saw this expression in a book and I cannot understand how did he get this expression.
Suppose $Z_t$ and $D_t$ are some stochastic processes and we have these expressions,
$Z_{t_k} - Z_{t_{k-1}} = ...
