6533b838fe1ef96bd12a5057
RESEARCH PRODUCT
On the optimal approximation rate of certain stochastic integrals
Heikki Seppäläsubject
Discrete mathematicsMathematics(all)Numerical AnalysisRegular sequencesGeneral MathematicsApplied MathematicsStochastic integralsNon linear approximationFunction (mathematics)CombinatoricsNon-linear approximationFunction compositionAnalysisMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2010-09-01 | Journal of Approximation Theory |