Konrad Viltersten wrote: > Suppose you start off with this expression. > V[W_t / t^2] > and you wish to show that it tends towards 0 as t->oo. > > What we tried is this rephrasal. > (1/t) * V[W_t / t] > Does it hold? > > And then, is it possible to use the fact that > lim t->oo (W_t / t) = 0 (a.s.) > and do a rewriting as follows? > > lim t->oo (V[W_t / t]) = V[lim t->oo (W_t / t)] >
1. V(a W_t) = a^2 V(W_t) for any scalar a.
2. Convergence a.s. cannot be converted to convergence in variance without some kind of "dominated convergence."