Random linear recursions with dependent coefficients
A. P. Ghosh, D. Hay, V. Hirpara, R. Rastegar, A. Roitershtein, A., Schulteis, and J. Suh
TL;DR
This paper studies a stochastic recurrence relation with dependent random coefficients, demonstrating that its stationary solution's distribution exhibits regularly varying tails at infinity.
Contribution
It extends the analysis of linear recursions to dependent coefficients, revealing tail behavior of the stationary distribution.
Findings
Stationary solution has regularly varying tails at infinity.
Dependent coefficients influence tail behavior.
Provides theoretical insights into non-i.i.d. linear recursions.
Abstract
We consider the equation R(n)=Q(n)+M(n) R(n-1), with random non-i.i.d. coefficients (Q(n),M(n)), and show that the distribution tails of the stationary solution to this equation are regularly varying at infinity.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Financial Risk and Volatility Modeling · Mathematical Dynamics and Fractals