computing probability ssrw Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Expectation of $T^2$ where $T$ is the absorption time at $a,−a$ of a simple random walk $S_n$Stopping time computations via martingalesSimple symmetric random walk - is my assumption correct?Computing a Finite ExpectationProbability of asymmetric random walk returning to the originMartingale: Show $pT<+infty =1$.Simple Random Walk: Hitting time of 1 is a.s. finitede Moivre’s martingale stopping time problemRecurrent/transient at $0$ random walk in $mathbbR^d$ is also recurrent/transient at any $x in mathbbR^d$Integrating with respect to random variable
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computing probability ssrw
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Expectation of $T^2$ where $T$ is the absorption time at $a,−a$ of a simple random walk $S_n$Stopping time computations via martingalesSimple symmetric random walk - is my assumption correct?Computing a Finite ExpectationProbability of asymmetric random walk returning to the originMartingale: Show $pT<+infty =1$.Simple Random Walk: Hitting time of 1 is a.s. finitede Moivre’s martingale stopping time problemRecurrent/transient at $0$ random walk in $mathbbR^d$ is also recurrent/transient at any $x in mathbbR^d$Integrating with respect to random variable
$begingroup$
Let $(S_n)_ngeq 0$ be a simple symmetric or asymmetric random walk with $S_0 =0$ and $S_n^* = max_mleq n S_m$. Assume that $n$ and $a$ are even positive integers, $b$ is an even integer, $b leq a leq n$, $2a-b leq n$.
How can I compute $P(S_n^* < a, S_n = b)$?
I'm having trouble understanding what the computation means and how I would go about it.
probability probability-theory
asked Apr 2 at 2:32
user123user123
192
$endgroup$
add a comment |
$begingroup$
Let $(S_n)_ngeq 0$ be a simple symmetric or asymmetric random walk with $S_0 =0$ and $S_n^* = max_mleq n S_m$. Assume that $n$ and $a$ are even positive integers, $b$ is an even integer, $b leq a leq n$, $2a-b leq n$.
How can I compute $P(S_n^* < a, S_n = b)$?
I'm having trouble understanding what the computation means and how I would go about it.
probability probability-theory
asked Apr 2 at 2:32
user123user123
192
$endgroup$
1
$begingroup$
The question is, what's the probability that your random walk ends up at $b$ at time $n$ without having reached the level $a$. You will want to look up the reflection principle.
$endgroup$
– Nate Eldredge
Apr 2 at 2:46
add a comment |
$begingroup$
Let $(S_n)_ngeq 0$ be a simple symmetric or asymmetric random walk with $S_0 =0$ and $S_n^* = max_mleq n S_m$. Assume that $n$ and $a$ are even positive integers, $b$ is an even integer, $b leq a leq n$, $2a-b leq n$.
How can I compute $P(S_n^* < a, S_n = b)$?
I'm having trouble understanding what the computation means and how I would go about it.
probability probability-theory
asked Apr 2 at 2:32
user123user123
192
$endgroup$
Let $(S_n)_ngeq 0$ be a simple symmetric or asymmetric random walk with $S_0 =0$ and $S_n^* = max_mleq n S_m$. Assume that $n$ and $a$ are even positive integers, $b$ is an even integer, $b leq a leq n$, $2a-b leq n$.
How can I compute $P(S_n^* < a, S_n = b)$?
I'm having trouble understanding what the computation means and how I would go about it.
probability probability-theory
probability probability-theory
asked Apr 2 at 2:32
user123user123
192
asked Apr 2 at 2:32
user123user123
192
asked Apr 2 at 2:32
user123user123
192
asked Apr 2 at 2:32
user123user123
192
asked Apr 2 at 2:32
user123user123
192
192
1
$begingroup$
The question is, what's the probability that your random walk ends up at $b$ at time $n$ without having reached the level $a$. You will want to look up the reflection principle.
$endgroup$
– Nate Eldredge
Apr 2 at 2:46
add a comment |
1
$begingroup$
The question is, what's the probability that your random walk ends up at $b$ at time $n$ without having reached the level $a$. You will want to look up the reflection principle.
$endgroup$
– Nate Eldredge
Apr 2 at 2:46
1
1
$begingroup$
The question is, what's the probability that your random walk ends up at $b$ at time $n$ without having reached the level $a$. You will want to look up the reflection principle.
$endgroup$
– Nate Eldredge
Apr 2 at 2:46
$begingroup$
The question is, what's the probability that your random walk ends up at $b$ at time $n$ without having reached the level $a$. You will want to look up the reflection principle.
$endgroup$
– Nate Eldredge
Apr 2 at 2:46
add a comment |
0
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$begingroup$
The question is, what's the probability that your random walk ends up at $b$ at time $n$ without having reached the level $a$. You will want to look up the reflection principle.
$endgroup$
– Nate Eldredge
Apr 2 at 2:46