• We are pleased to announce that the winner of our Feedback Prize Draw for the Winter 2024-25 session and winning £150 of gift vouchers is Zhao Liang Tay. Congratulations to Zhao Liang. If you fancy winning £150 worth of gift vouchers (from a major UK store) for the Summer 2025 exam sitting for just a few minutes of your time throughout the session, please see our website at https://www.acted.co.uk/further-info.html?pat=feedback#feedback-prize for more information on how you can make sure your name is included in the draw at the end of the session.
  • Please be advised that the SP1, SP5 and SP7 X1 deadline is the 14th July and not the 17th June as first stated. Please accept out apologies for any confusion caused.

Holding times

R

rajeev

Member
Hello Everyone...

In the computation of Holding times distribution for the continuous time
markov jump process there is a sequence of sets B's defined, which is a cantor
set and the set containg chain seems to be wrong i.e


B1 > B2 > B3....... is wrong it should be other way round........

and

{To > t} = lim Bn

needs an explanation........there seems to be the usage of density of cantor set..........



The derivation of holding time distribution for inhomogenuos case is
difficult..........if anybody is through with this please explain
 
Cantor Set

You're scaring me!! I've never heard of a Cantor set... What is it?!
 
In chapter six in holding times section we have

{To > t } = Intersection B

how did we get this and moreover the way the sets are defined...it should not be intersection of B's.....it should lim B
 
B1 is the set of events for which X(t/2) = X(t) = X(0).

B2 is the set of events for which X(t/4) = X(2t/4) = X(3t/4) = X(t) = X(0).

B3 is the set of events for which X(t/8) = X(2t/8) = X(3t/8) = ... = X(8t/8) = X(0).

And so on.

So B2 lies wholly within B1, B3 lies wholly within B2, etc.

The intersection of all the B's is the same as the limit as n goes to infinity.

So the course notes are correct here. Having said that, I think it's much easier to show that the first holding time is exponentially distributed by setting up a differential equation and solving it. This is what the alternative proof does.
 
Back
Top