2016年12月31日 · 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! $\endgroup$

2015年2月7日 · Answer to the second question: For the pointwise estimate, we can rely on the law of iterated logarithm (LIL). ). Indeed,

2019年11月16日 · However, I was unsure as to how to verify this output provided the study of random walks. I have that given a simple symmetric random walk, the probability of reaching some $\ b$ before $\ 0$ is defined as: $$\ P[W(a) \ hit \ 0 \ before \ b] = 1 - \frac{a}{b}$$ This, however, does not produce 0.04 when substituting $\ a, b$ in the argument. Any ...

2017年4月16日 · 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 enclosing square

2015年4月26日 · The gist of the transfer matrix approach is that we can list the "states" that a particular node in the cycle can have, figure out which state-to-state transitions are allowed moving from left to right on the number line, and express the number of ways to get from the left end of a cycle to the right end (i.e., the number of different cycles) in terms of a product of …

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 ...

2020年6月8日 · Obviously random walk satisfies both conditions. But there are many other models. Let us say we have a Markov chain on the state space $ \{ 0,1,2, \dotsc \} $ (we will argue soon that such a state space will be enough).

So, a lot of theory in symmetric random walks seems to concentrate on 'hitting/stopping times' and things like that. So I started wondering... How would I go about calculating the probability of n...

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