Random difference equations: an asymptotical result

• Published in: Journal of computational and applied mathematics Vol. 154; no. 1; pp. 183 - 193
• Main Authors: Chamayou, J.F, Dunau, J.L
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.05.2003; Elsevier
• Subjects: Dickman distribution; Difference and functional equations, recurrence relations; Differential–difference equations; Exact sciences and technology; Golomb's constant; Limit theorems; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Probability and statistics; Probability theory and stochastic processes; Pseudorandom numbers generation; Random difference equations; Random permutations; Sciences and techniques of general use; Shot noise; Differential–difference equations; primary: 60F; Golomb's constant; Random difference equations; Dickman distribution; Shot noise; Pseudorandom numbers generation; Random permutations; Transcendental equation; Golomb constant; Differential equation; Permutation; Recurrence relation; Probability theory; Asymptotic behavior; Pseudorandom number; Difference equation; Stochastic process; Numerical analysis; Random variable; Random number generation; Stochastic equation
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/S0377-0427(02)00821-X

we give a description of the model U n = X n (1+ U n−1 ) for n>1 in the case where the X i are i.i.d random variables with density αx α−1 on [0,1], (α>0) . We use it to generate recursively Dickman pseudorandom numbers ( α=1) and to simulate shot noise.