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arXiv · 2412.10068

Regional Fractional Stochastic Burgers from random interactions

Pedro Cardoso·Patrícia Gonçalves
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Abstract

The purpose of this article is to derive the crossover from the Ornstein-Uhlenbeck process to energy solutions of the stochastic Burgers equation with characteristic operators given in terms of fractional operators, such as the regional fractional Laplacian. The approach is to consider a boundary driven exclusion process with long jumps and asymmetric jump rates. Depending on the strength of the asymmetry we prove the convergence to stationary solutions of either the Ornstein-Uhlenbeck equation, or the stochastic Burgers equation. In the later setting, the convergence in some regimes is guaranteed by the recent proof of uniqueness of energy solutions derived in [16].

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Pedro Cardoso, Patrícia Gonçalves. 2024-12-13. Regional Fractional Stochastic Burgers from random interactions. https://arxiv.org/abs/2412.10068

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