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Nonnegative Superharmonic Function is Constant for $d>2$?
I have to do the following:
Let $\alpha>0$ be fixed, $(X_i)_{i\geq 1}$ be i.i.d., $\mathbb R^{d}$-valued random variables, uniformly distributed on the ball $B(0,a)$. Set $\displaystyle ...
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Superharmonic function and supermartingale
If $f$ is a nonnegative superharmonic function in dimension 2, how to prove that $f$ is constant?
There is an exercise in R.Durrett's probability book, which gives out a method to prove it by ...
