TY - GEN

T1 - On Monte Carlo and Quasi-Monte Carlo Methods for Series Representation of Infinitely Divisible Laws

AU - Kawai, Reiichiro

AU - Imai, Junichi

PY - 2012

Y1 - 2012

N2 - Infinitely divisible random vectors and Lévy processes without Gaussian component admit representations with shot noise series. To enhance efficiency of the series representation in Monte Carlo simulations, we discuss variance reduction methods, such as stratified sampling, control variates and importance sampling, applied to exponential interarrival times forming the shot noise series. We also investigate the applicability of the generalized linear transformation method in the quasi-Monte Carlo framework to random elements of the series representation. Although implementation of the proposed techniques requires a small amount of initial work, the techniques have the potential to yield substantial improvements in estimator efficiency, as the plain use of the series representation in those frameworks is often expensive. Numerical results are provided to illustrate the effectiveness of our approaches.

AB - Infinitely divisible random vectors and Lévy processes without Gaussian component admit representations with shot noise series. To enhance efficiency of the series representation in Monte Carlo simulations, we discuss variance reduction methods, such as stratified sampling, control variates and importance sampling, applied to exponential interarrival times forming the shot noise series. We also investigate the applicability of the generalized linear transformation method in the quasi-Monte Carlo framework to random elements of the series representation. Although implementation of the proposed techniques requires a small amount of initial work, the techniques have the potential to yield substantial improvements in estimator efficiency, as the plain use of the series representation in those frameworks is often expensive. Numerical results are provided to illustrate the effectiveness of our approaches.

UR - http://www.scopus.com/inward/record.url?scp=84893535050&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893535050&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-27440-4_26

DO - 10.1007/978-3-642-27440-4_26

M3 - Conference contribution

AN - SCOPUS:84893535050

SN - 9783642274398

T3 - Springer Proceedings in Mathematics and Statistics

SP - 471

EP - 486

BT - Monte Carlo and Quasi-Monte Carlo Methods 2010

PB - Springer New York LLC

T2 - 9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010

Y2 - 15 August 2010 through 20 August 2010

ER -