Skip to main content
MathOverflow

Return to Question

edited tags
Link
YCor
YCor
  • 63.9k
  • 5
  • 187
  • 286
Corrected maths
Source Link
edit approved Jul 2, 2021 at 10:14
Igor Sikora
edit approved Jul 2, 2021 at 10:14
Igor Sikora
  • 1.8k
  • 1
  • 11
  • 20

Let x(t+1) = x(t) + e(t)$x(t+1) = x(t) + e(t)$, e(t)$e(t)$ iid N(0,1)$\mathcal{N}(0,1)$. What is the probability of x(s)> c$x(s)> c$, for any 0<s<T$0<s<T$? Calculation for any specific s$s$ is easy. But I am looking for the probability that the random walk crosses c$c$ any time between now and T$T$. Easy to implement approximation preferred.

Let x(t+1) = x(t) + e(t), e(t) iid N(0,1). What is the probability of x(s)> c, for any 0<s<T? Calculation for any specific s is easy. But I am looking for the probability that the random walk crosses c any time between now and T. Easy to implement approximation preferred.

Let $x(t+1) = x(t) + e(t)$, $e(t)$ iid $\mathcal{N}(0,1)$. What is the probability of $x(s)> c$, for any $0<s<T$? Calculation for any specific $s$ is easy. But I am looking for the probability that the random walk crosses $c$ any time between now and $T$. Easy to implement approximation preferred.

Source Link
Martin Moryson
Martin Moryson
  • 1

Probability of random crossing a specific value any time

Let x(t+1) = x(t) + e(t), e(t) iid N(0,1). What is the probability of x(s)> c, for any 0<s<T? Calculation for any specific s is easy. But I am looking for the probability that the random walk crosses c any time between now and T. Easy to implement approximation preferred.