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arXiv · 2412.14781

Random additive perturbation of a $k$ term recurrence relation

Lisette Jager·Killian Verdure
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Abstract

We are interested in stochastic processes satisfying a nonlinear recurrence relation of the form $$X_{n + k} = \Phi_0 (X_n, ..., X_{n + k - 1}) + \Theta_n$$ where $\Theta$ is a noise term. We establish the existence of an invariant measure for this process under given sufficient conditions on $\Phi_0.$

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Lisette Jager, Killian Verdure. 2024-12-19. Random additive perturbation of a $k$ term recurrence relation. https://arxiv.org/abs/2412.14781

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