2D Random Walk Hitting Time
$begingroup$
Suppose there is a grid $[1,N]^2$. A person standing at some initial point $(x_0,y_0)$ walk randomly within the grid. At each location, he/she walks to a neighboring location with equal probability (e.g., for an interior point, the probability is $frac{1}{4}$; for a corner, it's $frac{1}{2}$.). Suppose there are $m$ absorbing barriers $B={(x_1,y_1),cdots,(x_m,y_m)}$ inside the grid. Once the person is on a barrier, the random walk process stops. I'd like to ask how to calculate the hitting probability and the expected number of steps for each barrier.
Edit: The problem can be transformed into a Markov chain. But the expected hitting time for each absorbing state is still not easy to calculate.
probability markov-chains random-walk
asked Dec 26 '18 at 11:20
Hang WuHang Wu
428310
$endgroup$
add a comment |
$begingroup$
Suppose there is a grid $[1,N]^2$. A person standing at some initial point $(x_0,y_0)$ walk randomly within the grid. At each location, he/she walks to a neighboring location with equal probability (e.g., for an interior point, the probability is $frac{1}{4}$; for a corner, it's $frac{1}{2}$.). Suppose there are $m$ absorbing barriers $B={(x_1,y_1),cdots,(x_m,y_m)}$ inside the grid. Once the person is on a barrier, the random walk process stops. I'd like to ask how to calculate the hitting probability and the expected number of steps for each barrier.
Edit: The problem can be transformed into a Markov chain. But the expected hitting time for each absorbing state is still not easy to calculate.
probability markov-chains random-walk
asked Dec 26 '18 at 11:20
Hang WuHang Wu
428310
$endgroup$
add a comment |
$begingroup$
Suppose there is a grid $[1,N]^2$. A person standing at some initial point $(x_0,y_0)$ walk randomly within the grid. At each location, he/she walks to a neighboring location with equal probability (e.g., for an interior point, the probability is $frac{1}{4}$; for a corner, it's $frac{1}{2}$.). Suppose there are $m$ absorbing barriers $B={(x_1,y_1),cdots,(x_m,y_m)}$ inside the grid. Once the person is on a barrier, the random walk process stops. I'd like to ask how to calculate the hitting probability and the expected number of steps for each barrier.
Edit: The problem can be transformed into a Markov chain. But the expected hitting time for each absorbing state is still not easy to calculate.
probability markov-chains random-walk
asked Dec 26 '18 at 11:20
Hang WuHang Wu
428310
$endgroup$
Suppose there is a grid $[1,N]^2$. A person standing at some initial point $(x_0,y_0)$ walk randomly within the grid. At each location, he/she walks to a neighboring location with equal probability (e.g., for an interior point, the probability is $frac{1}{4}$; for a corner, it's $frac{1}{2}$.). Suppose there are $m$ absorbing barriers $B={(x_1,y_1),cdots,(x_m,y_m)}$ inside the grid. Once the person is on a barrier, the random walk process stops. I'd like to ask how to calculate the hitting probability and the expected number of steps for each barrier.
Edit: The problem can be transformed into a Markov chain. But the expected hitting time for each absorbing state is still not easy to calculate.
probability markov-chains random-walk
probability markov-chains random-walk
asked Dec 26 '18 at 11:20
Hang WuHang Wu
428310
asked Dec 26 '18 at 11:20
Hang WuHang Wu
428310
edited Dec 27 '18 at 12:21
Hang Wu
asked Dec 26 '18 at 11:20
Hang WuHang Wu
428310
asked Dec 26 '18 at 11:20
Hang WuHang Wu
428310
asked Dec 26 '18 at 11:20
Hang WuHang Wu
428310
428310
add a comment |
add a comment |
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