PlanetMath: hitting time

(more info)

Math for the people, by the people.

donor list - find out how

Main Menu

hitting time

(Definition)

Let $(X_n)_{n\ge 0}$ be a Markov Chain. Then the hitting time for a subset $A$ of $I$ (the indexing set) is the random variable:

$\displaystyle H^A = \inf \{n\ge 0 : X_n\in A\}$

(set $\inf \varnothing = \infty$ .

This can be thought of as the time before the chain is first in a state that is a member of $A$

Wite $h_i^A$ for the probability that, starting from $i\in I$ the chain ever hits the set A:

$\displaystyle h_i^A = P(H^A <\infty : X_0 = i)$

When A is a closed class, $h_i^A$ is the absorption probability.

"hitting time" is owned by PrimeFan. [ full author list (2) | owner history (2) ]

(view preamble | get metadata)

Also defines:

absorption probability

Log in to rate this entry.
(view current ratings)

Cross-references: closed class, random variable, indexing set, subset, Markov chain

This is version 5 of hitting time, born on 2004-04-15, modified 2008-06-04.
Object id is 5764, canonical name is HittingTime.
Accessed 4295 times total.

Classification:

60J10 (Probability theory and stochastic processes :: Markov processes :: Markov chains with discrete parameter)

Pending Errata and Addenda

None.[ View all 1 ]

Discussion

forum policy

No messages.

Interact