Periodic solutions for stochastic differential inclusions

Benedetti Irene, Department of Mathematics and Computer Science, University of Perugia
Cretarola Alessandra , University of Perugia

We present existence results for mild solutions of semilinear stochastic differential inclusions subjected to periodic conditions with possible application to climate model studies. Indeed, to encompass the broadest possible range in climate change models, it is essential to consider non-deterministic differential equations. For example, cyclones can be treated as a rapidly varying component and represented as a white-noise process. In this context, nonlinear stochastic parabolic differential equations were initially proposed by North and Cahalan [1] to explore non-deterministic variability in energy balance climate frameworks. Climate models based on differential inclusions are characterized by a deterministic part, a stochastic part, or both, described by set-valued maps. Considering set-valued maps allows us to include in the model cases where the exact value of the empirical evidence cannot be calculated, but is known with a certain degree of uncertainty, see e.g. [2, 3]. Moreover, the periodic conditions may account for seasonal periodic changes. We show both the theoretical achievements and a possible application to climate change models. The talk is based on a joint paper with Alessandra Cretarola and Lorenzo Guida, University of Perugia. References [1] G.R. North, R.F. Cahalan, Predictability in a solvable stochastic climate model, J. Atmospheric Sci. 38 (1982) 504 – 513. [2] J.I. Díaz, J.A. Langa, J. Valero, On the asymptotic behavior of solutions of a stochastic energy balance climate model, Physica D, 238 (2009), 880 – 887. [3] G. Diaz, J.I. Diaz, Stochastic energy balance climate models with Legendre weighted diffusion and an additive cylindrical Wiener process forcing, DCDS-S, 15:10 (2022), 2837-2870.

Area: CS46 - Semilinear Stochastic Differential Equations in Infinite-Dimensional Spaces (Alessandra Cretarola)

Keywords: Stochastic differential inclusions, periodic stochastic process, climate change models

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