## Simulating Perpetuities (1999)

Venue: | Methodol. Comput. Appl. Probab |

Citations: | 9 - 3 self |

### BibTeX

@ARTICLE{Devroye99simulatingperpetuities,

author = {Luc Devroye},

title = {Simulating Perpetuities},

journal = {Methodol. Comput. Appl. Probab},

year = {1999},

volume = {3},

pages = {97--115}

}

### Years of Citing Articles

### OpenURL

### Abstract

. A perpetuity is a random variable that can be represented as 1 + W 1 + W 1 W 2 + W 1 W 2 W 3 + \Delta \Delta \Delta, where the W i 's are i.i.d. random variables. We study exact random variate generation for perpetuities and discuss the expected complexity. For the Vervaat family, in which W 1 L = U 1=fi , fi ? 0, U uniform [0; 1], all the details of a novel rejection method are worked out. There exists an implementation of our algorithm that only uses uniform random numbers, additions, multiplications and comparisons. Keywords and phrases. Random variate generation. Perpetuities. Rejection method. Simulation. Monte Carlo method. Expected time analysis. Probability inequalities. Infinite divisiblity. 1991 Mathematics Subject Classifications: Primary 65C10. Secondary 65C05, 11K45, 68U20. Authors' address: School of Computer Science, McGill University, 3480 University Street, Montreal, Canada H3A 2K6. The authors' research was sponsored by NSERC Grant A3456 and FCAR Grant 90-ER...