Optimal Importance Sampling for the Approximation of Integrals ...
Optimal Importance Sampling for the Approximation of Integrals Special Session on Monte Carlo Methods and Functional Analysis in Honor of Stefan Heinrich’s 60th Birthday
Aicke Hinrichs Friedrich-Schiller University Jena
MCQMC Warsaw 2010
Aicke Hinrichs
Optimal Importance Sampling
1 / 14
The Problem D ⊆ Rd Borel measurable % probability density on D H Hilbert space of functions f : D → R Integration Problem: Z I (f ) = f (x)%(x) dx D
Problem is well defined iff H ⊂ L1 (%) iff Z Z 1/2 init C = K (x, y )%(x)%(y ) dxdy
Aicke Hinrichs Friedrich-Schiller University Jena
MCQMC Warsaw 2010
Aicke Hinrichs
Optimal Importance Sampling
1 / 14
The Problem D ⊆ Rd Borel measurable % probability density on D H Hilbert space of functions f : D → R Integration Problem: Z I (f ) = f (x)%(x) dx D
Problem is well defined iff H ⊂ L1 (%) iff Z Z 1/2 init C = K (x, y )%(x)%(y ) dxdy
