Stochastic process questions

[Stefania Anastasopoulou]

Hello everyone!

Could you please explain to me what exactly the waiting time is and why it is exponentially distributed?

Also, in Chapter 3 could you please clarify the section of accident proneness?

ASAP Please!!

Thank you very much

 

[Harashima Senju]

Hello everyone!

Could you please explain to me what exactly the waiting time is and why it is exponentially distributed?

Also, in Chapter 3 could you please clarify the section of accident proneness?

ASAP Please!!

Thank you very much

Waiting time is the time spent in a state say i. The proof of why it is exponentially distributed is given in the notes chapter 5 page 11

 

[Stefania Anastasopoulou]

Thanks for your reply. Could you please explain to me how i can figure out if the Markov Chain is periodic or aperiodic? Could you please give me an example?

 

[John Potter]

Hi Stefania,

Your second question has nothing to do with the first one. It's worth posting separate questions as new posts in the future.

A Markov chain is periodic if return from a state to itself is ONLY possible in a multiple of k>1 steps.
Example
Draw this diagram
State A, arrows to B and C
State B arrow to D
State C arrow to D
State D arrow to A
You can only get from a state to itself in a multiple of 3 steps. So, it's a periodic chain.
A Markov chain is aperiodic if it is NOT periodic.
Draw an arrow from A to itself, aperiodic chain now

Good luck!
John