论文标题
Lindley递归的乘法版本
A Multiplicative Version of the Lindley Recursion
论文作者
论文摘要
本文介绍了随机递归的分析$ w_ {i+1} = [v_iw_i+y_i]^+$，可以解释为第1订单的自动回归过程，反映在0。我们通过对模型的稳定性条件的讨论开始我们的博览会。写作$ y_i = b_i-a_i $，对于非阴性i.i.d. \ \随机变量的独立序列$ \ {a_i \} _ {i \ in n_0} $和$ \ {b_i \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {i \ in_0} $}是I.I.D.序列也（独立于$ \ {a_i \} _ {i \ in n_0} $和$ \ {b_i \} _ {i \ in n_0} $），然后我们考虑三个特殊情况：（i）$ v_i $仅获得负值，并且只有$ b_i $ proganty probity proginal a $ equ a $ equ a $ equ a $ vi a $ vi a $ vi a $ vi a $ vi a $ vi a $ vi a $ vi a $ vi a $ vi a $ vi a $ Vi a $ vi a $ vi a $ vi a $ vi a。 $ p \ in（0,1）$，否则为负，$ a_i $和$ b_i $均具有合理的lst，（iii）$ v_i $均在$ [0,1] $上均匀分发，并且$ a_i $均为指数分布。在所有三种情况下，我们得出瞬态和固定结果，其中瞬态结果是根据几何分布的时期的变换而言。
This paper presents an analysis of the stochastic recursion $W_{i+1} = [V_iW_i+Y_i]^+$ that can be interpreted as an autoregressive process of order 1, reflected at 0. We start our exposition by a discussion of the model's stability condition. Writing $Y_i=B_i-A_i$, for independent sequences of non-negative i.i.d.\ random variables $\{A_i\}_{i\in N_0}$ and $\{B_i\}_{i\in N_0}$, and assuming $\{V_i\}_{i\in N_0}$ is an i.i.d. sequence as well (independent of $\{A_i\}_{i\in N_0}$ and $\{B_i\}_{i\in N_0}$), we then consider three special cases: (i) $V_i$ attains negative values only and $B_i$ has a rational LST, (ii) $V_i$ equals a positive value $a$ with certain probability $p\in (0,1)$ and is negative otherwise, and both $A_i$ and $B_i$ have a rational LST, (iii) $V_i$ is uniformly distributed on $[0,1]$, and $A_i$ is exponentially distributed. In all three cases we derive transient and stationary results, where the transient results are in terms of the transform at a geometrically distributed epoch.
