On the Growth Rate of a Linear Stochastic Recursion with Markovian Dependence

Pirjol Dan; Zhu Lingjiong

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On the Growth Rate of a Linear Stochastic Recursion with Markovian Dependence

机译：马尔可夫相关性的线性随机递归的增长率

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We consider the linear stochastic recursion where the multipliers are random and have Markovian dependence given by the exponential of a standard Brownian motion and are i.i.d. positive random noise independent of . Using large deviations theory we study the growth rates (Lyapunov exponents) of the positive integer moments with . We show that the Lyapunov exponents exist, under appropriate scaling of the model parameters, and have non-analytic behavior manifested as a phase transition. We study the properties of the phase transition and the critical exponents using both analytic and numerical methods.

机译：我们考虑线性随机递归，其中乘数是随机的，并且具有由标准布朗运动的指数给出的马尔可夫依赖关系，即i.d.正随机噪声无关。我们使用大偏差理论研究具有的正整数矩的增长率（李雅普诺夫指数）。我们表明，在适当缩放模型参数的情况下，存在Lyapunov指数，并且具有表现为相变的非分析行为。我们使用解析和数值方法研究相变和临界指数的性质。

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《Journal of Statistical Physics》 |2015年第5期|共35页
作者
Pirjol Dan; Zhu Lingjiong;
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正文语种 eng
中图分类统计物理学;
关键词
Linear stochastic recursion; Lyapunov exponent; Phase transitions; Critical exponent; Large deviations;

机译：线性随机递归;李雅普诺夫指数;相变;临界指数;大偏差;

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1. On the Growth Rate of a Linear Stochastic Recursion with Markovian Dependence [J] . Pirjol Dan, Zhu Lingjiong Journal of Statistical Physics . 2015,第5期

机译：马尔可夫相关性的线性随机递归的增长率
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7. On the growth rate of a linear stochastic recursion with Markovian dependence [O] . Pirjol, Dan, Zhu, Lingjiong 2015

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8. Markovian Queueing Systems with Stochastically Varying Arrival Rates. [R] . Yadin, M. 1977

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On the Growth Rate of a Linear Stochastic Recursion with Markovian Dependence

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