A stochastic process that describes a path arising from a succession of random steps.
Questions tagged [random-walk]
250 questions
39
votes
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Why does the variance of the Random walk increase?
The random walk that is defined as $Y_{t} = Y_{t-1} + e_t$, where $e_t$ is white noise. Denotes that the current position is the sum of the previous position + an unpredicted term.
You can prove that the mean function $\mu_t = 0 $, since
$$E(Y_{t})…
Isbister
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Random walk on the edges of a cube
An ant is placed in a corner of a cube and cannot move. A spider starts from the opposite corner, and can move along the cube's edges in any direction $(x,y,z)$ with equal probability $1/3$. On average, how many steps will the spider need to get to…
Elizabeth Susan Joseph
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Why are random walks intercorrelated?
I have observed that, on average, the absolute value of Pearson correlation coefficient is a constant close to 0.560.42 for any pair of independent random walks, regardless of the walk length.
Can someone explain this phenomenon?
I expected the…
Adam
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Hamiltonian Monte Carlo vs. Sequential Monte Carlo
I am trying to get a feel for the relative merits and drawbacks, as well as different application domains of these two MCMC schemes.
When would you use which and why?
When might one fail but the other not (e.g. where is HMC applicable but SMC…
Astrid
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The magic money tree problem
I thought of this problem in the shower, it was inspired by investment strategies.
Let's say there was a magic money tree. Every day, you can offer an amount of money to the money tree and it will either triple it, or destroy it with 50/50…
ElectronicToothpick
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MCMC on a bounded parameter space?
I am trying to apply MCMC on a problem, but my priors(in my case they are $\alpha\in[0,1],\beta\in[0,1]$)) are restricted to an area? Can I use normal MCMC and ignore the samples that fall outside of the restricted zone(which in my case is [0,1]^2),…
Cupitor
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Random walk with momentum
Consider an integer random walk starting at 0 with the following conditions:
The first step is plus or minus 1, with equal probability.
Every future step is: 60% likely to be in the same direction as
the previous step, 40% likely to be in the…
user1566
16
votes
2 answers
What does it mean to say that an event "happens eventually"?
Consider a 1 dimensional random walk on the integers $\mathbb{Z}$ with initial state $x\in\mathbb{Z}$:
\begin{equation}
S_n=x+\sum^n_{i=1}\xi_i
\end{equation}
where the increments $\xi_i$ are I.I.D such that…
Ye Tian
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13
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Intuition of Random Walk having a constant mean
I am very new to time series analysis.
A random walk is defined as $Y_t=\phi Y_{t-1}+\varepsilon_t$, where $\phi=1$ and $\varepsilon_t$ is white noise. It is said that process is non-stationary for its variance is not constant. However, the mean is…
koyamashinji
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What is the autocorrelation for a random walk?
Seems like it is really high, but this is counterintuitive to me. Can somebody please explain? I am very confused by this issue and would appreciate a detailed, insightful explanation.
Thanks a lot in advance!
The Baron
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Why is an unbiased random walk non-ergodic?
Wikipedia says "An unbiased random walk is non-ergodic."
Let's look at a simple random walk. It's defined as: take independent random variables $Z_{1},Z_{2}$, where each variable is either $1$ or $−1,$ with a 50% probability for either value, and…
Alex Craft
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Why is a random walk not a stationary process?
In the book Analysis of Financial Time Series by Rue Tsay, I read:
A time series $\{p_t\}$ is a random walk if it satisfies $p_t = p_{t−1} + a_t$
where $p_0$ is a real number denoting the starting value of the process
and $\{a_t\}$ is a white…
Victor
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Random walk estimation with AR(1)
When I estimate a random walk with an AR(1), the coefficient is very close to 1 but always less.
What is the math reason that the coefficient is not greater than one?
Marco
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Computing the cumulative distribution of max drawdown of random walk with drift
I am interested in the distribution of the maximum drawdown of a random walk: Let $X_0 = 0, X_{i+1} = X_i + Y_{i+1}$ where $Y_i \sim \mathcal{N}(\mu,1)$. The maximum drawdown after $n$ periods is $\max_{0 \le i \le j \le n} (X_i - X_j)$. A paper by…
shabbychef
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Random walk: kings on a chessboard
I have a question about the random walk of two kings in a 3×3 chessboard.
Each king is moving randomly with equal probability on this chessboard - vertically, horizontally and diagonally. Τhe two kings are moving independently from each other in the…
cube
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