Search results for "Non linear approximation"

On the optimal approximation rate of certain stochastic integrals

2010

AbstractGiven an increasing function H:[0,1)→[0,∞) and An(H)≔infτ∈Tn(∑i=1n∫ti−1ti(ti−t)H(t)2dt)12, where Tn≔{τ=(ti)i=0n:0=t0<t1<⋯<tn=1}, we characterize the property An(H)≤cn, and give conditions for An(H)≤cnβ and An(H)≥1cnβ for β∈(0,1), both in terms of integrability properties of H. These results are applied to the approximation of stochastic integrals.