Computing Invariant Densities of a Class of Piecewise Increasing Mappings

Zi Wang, Jiu Ding, N. Rhee
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Abstract

Let [Formula: see text] be a piecewise increasing mapping satisfying some generalized convexity condition, so that it possesses an invariant density that is a decreasing function. We show that this invariant density can be computed by a family of Markov finite approximations that preserve the monotonicity of integrable functions. We also construct a quadratic spline Markov method and demonstrate its merits numerically.
一类分段递增映射的不变密度计算
设[公式:见文]为满足某些广义凸性条件的分段递增映射,使其具有不变密度为递减函数。我们证明了这种不变密度可以用一组保持可积函数单调性的马尔可夫有限近似来计算。构造了二次样条马尔可夫方法,并用数值方法证明了其优点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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