Name
Abstract | ||
|---|---|---|
In this paper we study a reflected AR(1) process, i.e. a process (Z(n))(n) obeying the recursion Z(n+1) = max{aZ(n) + X-n, 0}, with (X-n)(n) a sequence of independent and identically distributed (i.i.d.) random variables. We find explicit results for the distribution of Z(n) (in terms of transforms) in case X-n can be written as Y-n - B-n, with (B-n) n being a sequence of independent random variables which are all Exp(lambda) distributed, and (Y-n)(n) i.i.d.; when vertical bar a vertical bar < 1 we can also perform the corresponding stationary analysis. Extensions are possible to the case that (B-n)(n) are of phase-type. Under a heavy-traffic scaling, it is shown that the process converges to a reflected Ornstein-Uhlenbeck process; the corresponding steady-state distribution converges to the distribution of a normal random variable conditioned on being positive. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1017/jpr.2016.42 | JOURNAL OF APPLIED PROBABILITY |
Keywords | Field | DocType |
Reflected process, queueing, scaling limit | Autoregressive model,Combinatorics,Normal distribution,Random variable,Scaling limit,Independent and identically distributed random variables,Statistics,Scaling,Mathematics,Lambda,Stationary analysis | Journal |
Volume | Issue | ISSN |
53 | 3 | 0021-9002 |
Citations | PageRank | References |
2 | 0.40 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| o j boxma | 1 | 2 | 1.07 |
| Michel Mandjes | 2 | 534 | 73.65 |
| Josh E. Reed | 3 | 12 | 2.42 |