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woundedtiger4
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In probability, What is drift? I have tried to google but unfortunately I can't find the definition :(
Does it mean a movement from one point to an other point, for example in symmetric random walk: let's say that ω=ω_1ω_2ω_3... is the infinite sequence of coin tosses (p the pobability of Head "H" on each toss, and q=1-p the probability of Tail "T" on each toss, are both equal to 1/2).
Let,
X_j={+1 if ω_j=H, -1 ifω_j=T
and define M_0=0,
M_K= Ʃ(j=1, k) X_j , k=0,1,2,3,...
The process M_k, k=0,1,2,3,... is a symmetric random walk.
In this example, can we say that when the position changes from M_1 to M_2 then that change is called as drift?
Thanks in advance.
Edited note:
OK, I found the following definition on wiki:
In probability theory, stochastic drift is the change of the average value of a stochastic (random) process. A related term is the drift rate which is the rate at which the average changes. This is in contrast to the random fluctuations about this average value. For example, the process which counts the number of heads in a series of n coin tosses has a drift rate of 1/2 per toss.
Now I understand that what is drift rate but I am still clueless about stochastic drift (or just "drift").
Does it mean a movement from one point to an other point, for example in symmetric random walk: let's say that ω=ω_1ω_2ω_3... is the infinite sequence of coin tosses (p the pobability of Head "H" on each toss, and q=1-p the probability of Tail "T" on each toss, are both equal to 1/2).
Let,
X_j={+1 if ω_j=H, -1 ifω_j=T
and define M_0=0,
M_K= Ʃ(j=1, k) X_j , k=0,1,2,3,...
The process M_k, k=0,1,2,3,... is a symmetric random walk.
In this example, can we say that when the position changes from M_1 to M_2 then that change is called as drift?
Thanks in advance.
Edited note:
OK, I found the following definition on wiki:
In probability theory, stochastic drift is the change of the average value of a stochastic (random) process. A related term is the drift rate which is the rate at which the average changes. This is in contrast to the random fluctuations about this average value. For example, the process which counts the number of heads in a series of n coin tosses has a drift rate of 1/2 per toss.
Now I understand that what is drift rate but I am still clueless about stochastic drift (or just "drift").
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