Examples of Random Recurrences in Closed Form

✍ Scribed by J.F. Chamayou

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 232 KB
• Volume: 16
• Category: Article
• ISSN: 0196-8858
• DOI: 10.1006/aama.1995.1021

✦ Synopsis

Various models with application to soil erosion, riverflow, and solar energy storage give rise to the random recurrence relation (X_{n+1}=\max \left(U_{n} X_{n}, Y_{n}\right), n \geq 0), where the (X_{01},\left(U_{n}\right){n-1}^{x}) and (\left(Y{n}\right){n=11}^{x}) are positive independent random variables with the (U{n} \mathbf{d} U_{0}) and (Y_{n} \mathbf{d} Y_{0}). Examples where the limit distribution of (X_{n}(n \rightarrow x)) can be calculated in closed form are presented for various distributions of (U_{11}) and (Y_{10}). (c) 1995 Aćademic Préss, Inc