palace
May9-10, 04:55 PM
Given a simple random walk X_n started at 1, and stopped the first time it hits zero (so it could be something like 1,2,1,2,3,2,1,0,0,0,0,0....) i would like to determine whether E(f(X_n)) is bounded or not for f(x) = x log log x and f(1)=f(2)=0...
I tried using jensens inequality for convexity of f(x) but it lead me nowhere and I'm at a loss of what to do now. Can i justify exchanging sup with E using dominated convergence or something? Any guidance would be appreciated thank you
I tried using jensens inequality for convexity of f(x) but it lead me nowhere and I'm at a loss of what to do now. Can i justify exchanging sup with E using dominated convergence or something? Any guidance would be appreciated thank you