Tagged Questions
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0answers
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Dimension free Concentration bounds for Martingales
Consider the following random process which is defined on $n$ numbers $0\leq x_1,\ldots,x_n\leq 1$:
At each step, pick an arbitrary number, say $x_i$. Then randomly (and independently) change its ...
1
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1answer
38 views
Asymmetric random walk with unequal step size other than 1.
Say, an asymmetric random walk, at each step it goes left by 1 step with chance $p$, and goes right by $a$ steps with chance $1-p$. (where $a$ is positive constant).
The chain stops whenever it ...
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0answers
54 views
Martingale with reflecting barrier
I am not very familiar with the theory of martingales or random walks, perhaps someone could point me in the right direction or give me some help with the following problem.
Consider a random ...
0
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1answer
195 views
Stopping time and random walk: Proof that Stopping time of reaching a certain value is finite a.s. [duplicate]
Possible Duplicate:
Proving that 1- and 2-d simple symmetric random walks return to the origin with probability 1
This is a basic question but I was wondering if there was a simple proof (I ...
2
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1answer
214 views
Non-symmetric simple random walk stopping time
Say there is a random walk $\{S_n\}$ with $S_0=0$ and $0<p=P(S_1=1)<\frac{1}{2}$. We know such a random walk would go to $-\infty$ eventually. Define the stopping time $T=\inf\{n: S_n=-\infty\}$, ...
1
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2answers
397 views
What are some martingales for asymmetric random walks?
Here are some examples for symmetric ones:
http://mathoverflow.net/questions/55092/martingales-in-both-discrete-and-continuous-setting/55101#55101
Is there a similar list for asymmmetric random ...
4
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1answer
247 views
Expectation of $TS_T$ where $T$ is the absorption time at $\{a,-a\}$ of a simple symmetric random walk $\{S_n\}$
I was trying to calculate the expectation of $T^2$ using some martingale and got that I needed the expectation of $TS_T$. Any idea?
