Multidimensional Diffusion Models - Computational Methods for Quantitative Finance - page 194

pricing of basket options in up to 5 dimensions. The construction of the sparse
tensor product space V L can be further developed to general sparse approximation
spaces

V L,β :=

W 1 ⊗···⊗ W d ,

β | | ∞ −| | ≥ βL − (L + d − 1 ) 1

d . Griebel and Knapek show in [75] that using such approx-
imation spaces one can remove the logarithmic term L d − 1 . Indeed, for 0 <β< 1,
one has dim V L,β = O

where β ∈ R and ∈ N

( 2 L ) . Furthermore, they have similar approximation proper-

ties as V L .