Dec 31, 2016 · Probability of random walk reaching one threshold before another using recurrence relation. 1.

Then $\alpha = P($ the walk hits $1$ before $-\infty)$. So by conditioning on the first step, we see that $\alpha = p + (1-p)\alpha^2$ which we can solve. Very concise indeed! $\endgroup$

Dec 9, 2021 · Simple Random Walk, proving variance of the walk at a stopping time. 1.

I have looked at many places but I have rarely found a full proof for the simple random walk case (I have found lots of document that state it for stochastic process / brownian motion, etc. ). So …

Expected hitting time in at least one walk with multiple 1-side bounded simple random walks Hot Network Questions How do I mitigate fallout of business downtime due wrongfully applied …

Apr 16, 2017 · Random walk: Need intuition behind the expected distance from origin versus expected deviation of the fraction of left/right steps. 4 2d random walk: expected time to hit …

Feb 7, 2015 · Answer to the second question: For the pointwise estimate, we can rely on the law of iterated logarithm (LIL). ). Indeed,

Consider a random walk on the integer number line $\mathbb Z$-axis, starting at position $0$. At each step, we move right with probability $ p $ and left with probability $ 1 - p $. What is the ...

Next, the probability that simple random walk in two dimensions -- call this $\rho_2(2n)$-- is at $0$ after $2n$ steps is the square of the previous probability. Consider the simple random walk …

Consider a simple symmetric random walk on the integer line starting from $0$ and, for some integers $-a ...