Investigation of linear difference equations with random effects

Advances in Difference Equations

Mehmet Merdan¹  Şeyma Şişman¹ 

[1] Department of Mathematical Engineering, Gümüşhane University, 29100, Gümüşhane, Turkey;

关键词: Linear difference equations;    Expected value;    Variance;    Z-transform method;   

DOI  :  10.1186/s13662-020-03018-9

来源: Springer

【 摘 要 】

In this study, random linear difference equations obtained by transforming the components of deterministic difference equations to random variables are investigated. Uniform, Bernoulli, binomial, negative binomial (or Pascal), geometric, hypergeometric and Poisson distributions have been used for the random effects for obtaining the random behavior of linear difference equations. The random version of the Z-transform, the RZ-transform, has been used to obtain an approximation for the random linear difference equation. Approximate expected values and variances are calculated by using the RZ-transform. The results have been obtained with Maple and are shown in graphs. It is shown that the random Z-transform is an effective tool for the investigation of random linear difference equations.

【 授权许可】

CC BY