2024/12/13 by Pedro Cardoso, Patrícia Gonçalves, Cardoso, Pedro +1 · 1 citation
Economics, Econometrics and Finance · #Stochastic processes and financial applications #Complex Systems and Time Series Analysis #Financial Risk and Volatility Modeling
paper · pdf · doi:10.48550/arxiv.2412.10068
The purpose of this article is to derive the crossover from the\nOrnstein-Uhlenbeck process to energy solutions of the stochastic Burgers\nequation with characteristic operators given in terms of fractional operators,\nsuch as the regional fractional Laplacian. The approach is to consider a\nboundary driven exclusion process with long jumps and asymmetric jump rates.\nDepending on the strength of the asymmetry we prove the convergence to\nstationary solutions of either the Ornstein-Uhlenbeck equation, or the\nstochastic Burgers equation. In the later setting, the convergence in some\nregimes is guaranteed by the recent proof of uniqueness of energy solutions\nderived in [16].\n