# Comparison of stochastic processes at a random time 2

• Aug 1st 2010, 09:15 AM
tossifan
Comparison of stochastic processes at a random time 2
Let $\displaystyle X_t$ and $\displaystyle Y_t$, $\displaystyle t \in \mathbb{N}$, be two discrete-time Markov chains such that $\displaystyle Pr(X_t\ge x) \le Pr(Y_t\ge x)$, for all $\displaystyle x$. Let $\displaystyle T$ be a non-negative random variable in $\displaystyle \mathbb{N}$ (T may depend on X and Y).

Is it true that $\displaystyle Pr(X_T\ge x) \le Pr(Y_T\ge x)$ ?

Thanks
• Aug 1st 2010, 11:11 AM
user
Good morning. Please can you help me to solve this exercise?. I must to use limiting distribution and change of variable. Thank you my friend.
Let Yn denote the nth order statistic, with Yn=qXn:n – ln(n), of a random sample X1,X2,…………..Xn from a exponential distribution Xi~exp(q). Find the limiting distribution of Yn.
• Aug 3rd 2010, 01:43 AM
tossifan
I think that still conditioning over T it should be ok, right?
• Aug 3rd 2010, 07:52 AM
SpringFan25
yes i would think so.