2024/08/01 by Yibo Wang, Wang, Yibo, Wanrong Cao +1
Economics, Econometrics and Finance · Social Sciences · #Stochastic processes and financial applications #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management
paper · pdf · doi:10.48550/arxiv.2408.00951
We investigate numerical approximations for the stochastic Burgers equation driven by an additive cylindrical fractional Brownian motion with Hurst parameter H ∈ ((1)/(2), 1). To discretize the continuous problem in space, a spectral Galerkin method is employed, followed by the presentation of a nonlinear-tamed accelerated exponential Euler method to yield a fully discrete scheme. By showing the exponential integrability of the stochastic convolution of the fractional Brownian motion, we present the boundedness of moments of semi-discrete and full-discrete approximations. Building upon these results and the convergence of the fully discrete scheme in probability proved by a stopping time technique, we derive the strong convergence of the proposed scheme.