Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Latin supercube sampling for very high-dimensional simulations
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Continuous random variate generation by fast numerical inversion
ACM Transactions on Modeling and Computer Simulation (TOMACS)
SIAM Journal on Scientific Computing
Random variate generation by numerical inversion when only the density is known
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On simulation of tempered stable random variates
Journal of Computational and Applied Mathematics
Quasi-Monte Carlo Method for Infinitely Divisible Random Vectors via Series Representations
SIAM Journal on Scientific Computing
Hi-index | 7.29 |
Infinitely divisible random vectors without Gaussian component admit representations with shot noise series. We analyze four known methods of deriving kernels of the series and reveal the superiority of the inverse Levy measure method over the other three methods for simulation use. We propose a numerical approach to the inverse Levy measure method, which in most cases provides no explicit kernel. We also propose to apply the quasi-Monte Carlo procedure to the inverse Levy measure method to enhance the numerical efficiency. It is known that the efficiency of the quasi-Monte Carlo could be enhanced by sensible alignment of low discrepancy sequence. In this paper we apply this idea to exponential interarrival times in the shot noise series representation. The proposed method paves the way for simulation use of shot noise series representation for any infinite Levy measure and enables one to simulate entire approximate trajectory of stochastic differential equations with jumps based on infinite shot noise series representation. Although implementation of the proposed method requires a small amount of initial work, it is applicable to general Levy measures and has the potential to yield substantial improvements in simulation time and estimator efficiency. Numerical results are provided to support our theoretical analysis and confirm the effectiveness of the proposed method for practical use.