Questions tagged [random-walk]

A stochastic process that describes a path arising from a succession of random steps.

286 questions
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3-D random walk: average distance after N steps

I am calculating the average distance in a 3-D random walk process after N steps. Each step is one unit long and the angle is randomly distributed around the origin. After N steps, what is the average distance from the origin? The $X,Y,Z$…
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Non-normal random walks

I'm aware of the simple 'proof' that shows random walks with a normal error term are non-stationary in original form and stationary in first-difference form but what happens if the errors have a different distribution? I'm looking into modelling…
user40124
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Random Walk Process in Time Series

Is it true that the mean of a random walk process does not depend on time and the sequence can be considered mean stationary?
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Random walk under changing conditions

I have a random walk where by at certain times or conditions the increments follow one distribution, and then another distribution under different conditions - how can I model this random walk (states can have fixed or random probabilities) For…
user40124
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Difference between arithmetic vs geometric random walk

I have read about arithmetic and geometric random walks. What is the difference between them?
Josh
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Random Walk with Restart vs. Personalized Pagerank

Are Personalized Pagerank and Random Walk with Restart really the same thing? From this source, it seems to be: http://web.eecs.umich.edu/~dkoutra/papers/fabp_pkdd2011.pdf I've used the RANKS RWR function and the igraph personalized page.rank…
Josh
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Probability that a simple 1d random walk is between [-k,k] in 100 moves

What is the probability that a simple 1d random walk is between (-k,k), exclusive, in 100 moves? My initial though was: $1-\sum_{i=k}^{100}P_i$, where $P_i$ stands for the probability that it reaches $k$ in $i$ number of moves.
user334639
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Is every time series that is not predictable a random walk?

The title already reveals my question. I was wondering how specific the characterisitics of a random walk are defined and if every time series that is not predictable belongs to the class of random walks. Edit: unpredictable in a sense that the past…
J3lackkyy
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Calculate 1D Random Walk Expected Iterations to return to origin

I'm trying to solve a stats problem as outlined below; I'm a bit new, however, and I'm not sure how I could solve this problem. Assume someone has lost their keys, and uses an inefficient random walk to search. He starts at 0, and moves 1 unit to…
user55322
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Random walks with momentum

I am interested in random walks with momentum in 1D, ie., random walks in which there is a certain probability $p$ to take a step in the same direction as the last step, and a probability $q = 1-p$ to take a step in the other direction (switch…
Jens
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Probability of a pattern in a random walk

Consider the discrete time random walk process such that $X_{t+1} = X_t + \epsilon_t$ where $X_0 = 0$ and $\epsilon_t$, is drawn from a symmetric distribution about $0$, such as the normal distribution. Given this sequence of points $(X_t)_{t \geq…
Aero
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experimenting random price movement

Random price movement Consider the following: The price of an apple starts at 1 dollar. On each day, the price will change -10% or +10%, with equal probability. You buy this apple on day 1, and sell on day N. What is your probability of losing money…
em1971
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