represents a random walk on a line with the probability of a positive unit step p and the probability of a negative unit step 1-p.
represents a random walk with the probability of a positive unit step p, the probability of a negative unit step q, and the probability of a zero step 1-p-q.
- RandomWalkProcess is also known as a lattice random walk.
- RandomWalkProcess is a discrete-time and discrete-state random process.
- RandomWalkProcess[p] value at time t follows TransformedDistribution[2 x-t,xBinomialDistribution[t,p]].
- RandomWalkProcess allows p and q to be real numbers between 0 and 1 such that p+q≤1.
- RandomWalkProcess can be used with such functions as Mean, PDF, Probability, and RandomFunction.
Examplesopen allclose all
Basic Examples (3)
Basic Uses (5)
Process Slice Properties (6)
Moment has no closed form for symbolic order:
FactorialMoment and its generating function:
A particle starts at the origin and moves to the right by one unit with probability and to the left by one unit with probability after each second. Find the probability that it has moved to the right by four units after 20 seconds:
Properties & Relations (6)
RandomWalkProcess is not weakly stationary:
The correlation function of a random walk process is the same as of WienerProcess:
Univariate slice distribution is related to BinomialDistribution:
Compare with the CDF of the TransformedDistribution of a binomial distribution:
In the limit the ratio has ArcSinDistribution:
Wolfram Research (2012), RandomWalkProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/RandomWalkProcess.html.
Wolfram Language. 2012. "RandomWalkProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RandomWalkProcess.html.
Wolfram Language. (2012). RandomWalkProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RandomWalkProcess.html