In this paper we study a fractional stochastic heat equation on Rd （d 〉 1） with additive noise /t u（t, x） = Dα/δ u（t, x）＋ b（u（t, x） ） ＋ WH （t, x） where D α/δ is a nonlocal fractional differential...In this paper we study a fractional stochastic heat equation on Rd （d 〉 1） with additive noise /t u（t, x） = Dα/δ u（t, x）＋ b（u（t, x） ） ＋ WH （t, x） where D α/δ is a nonlocal fractional differential operator and W H is a Gaussian-colored noise. We show the existence and the uniqueness of the mild solution for this equation. In addition, in the case of space dimension d = 1, we prove the existence of the density for this solution and we establish lower and upper Gaussian bounds for the density by Malliavin calculus.展开更多
基金Supported by NNSFC(11401313)NSFJS(BK20161579)+2 种基金CPSF(2014M560368,2015T80475)2014 Qing Lan ProjectSupported by MEC Project PAI80160047,Conicyt,Chile
文摘In this paper we study a fractional stochastic heat equation on Rd （d 〉 1） with additive noise /t u（t, x） = Dα/δ u（t, x）＋ b（u（t, x） ） ＋ WH （t, x） where D α/δ is a nonlocal fractional differential operator and W H is a Gaussian-colored noise. We show the existence and the uniqueness of the mild solution for this equation. In addition, in the case of space dimension d = 1, we prove the existence of the density for this solution and we establish lower and upper Gaussian bounds for the density by Malliavin calculus.
