A Few Random Walk Questions
Okay, so you've got your standard random walk:
Flip a coin. If heads, move one unit right, if not, one unit left. Start at x=0
The chance you will eventually get to x=1 approaches 1 as the number of additional flips you are willing to take approaches infinity, correct?
And again the chance you will eventually make it to say x=100 (or any other whole number) approaches 1 as the number of flips you are willing to take approaches infinity, correct?
I'm pretty sure the answer is yes and yes so far. How about this though:
You start off at x=1
Flip a coin. If heads, increase value by 10%. If tails, decrease value by 10%. Given you are prepared to flip forever, what are the chances you will make it to x=1.1 or higher? Is it 100% ?
If it is 100%, what if you start at x=1 and use a log-normal distribution (which yields an average change of 0) to figure out where your next step lands you. Will you always make it to a value greater than x=1 eventually ?
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