Details

Autor(en) / Beteiligte

• Gu, Yu
• Tsai, Li-Cheng

Titel

ANOTHER LOOK INTO THE WONG–ZAKAI THEOREM FOR STOCHASTIC HEAT EQUATION

Ist Teil von

• The Annals of applied probability, 2019-10, Vol.29 (5), p.3037-3061

Ort / Verlag

Hayward: Institute of Mathematical Statistics

Erscheinungsjahr

2019

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• For the heat equation driven by a smooth, Gaussian random potential: ∂ t u ε = 1 2 Δ u ε + u ε ( ξ ε − c ε ) , t > 0, x ∈ ℝ, where ξε converges to a spacetime white noise, and cε is a diverging constant chosen properly, we prove that uε converges in Ln to the solution of the stochastic heat equation for any n ≥ 1. Our proof is probabilistic, hence provides another perspective of the general result of Hairer and Pardoux (J. Math. Soc. Japan 67 (2015) 1551–1604), for the special case of the stochastic heat equation.We also discuss the transition from homogenization to stochasticity.