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arXiv · 2111.10801

Stochastic energy balance climate models with Legendre weighted diffusion and a cylindrical Wiener process forcing

Gregorio Díaz·Jesús Ildefonso Díaz
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Abstract

We consider a class of one-dimensional nonlinear stochastic parabolic problems associated with Sellers and Budyko diffusive energy balance climate models with a Legendre weighted diffusion and an additive cylindrical Wiener processes forcing. Our results use in an important way that, under suitable assumptions on the Wiener processes, a suitable change of variables leads the problem to a pathwise random PDE, hence an essentially "deterministic" formulation depending on a random parameter. Two applications are also given: the stability of solutions when the Wiener process converges to zero and the asymptotic behaviour of solutions for large time.

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Gregorio Díaz, Jesús Ildefonso Díaz. 2021-12-22. Stochastic energy balance climate models with Legendre weighted diffusion and a cylindrical Wiener process forcing. https://arxiv.org/abs/2111.10801

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