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
Using multiple stochastic integrals and the stochastic calculus for the frac-tional Brownian sheet, we define and we analyze the 2D-fractional stochastic currents.
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.
基金Partially supported by the ANR grant "Masterie" BLAN 012103Support by the CNCS grant "PN-II-ID-PCE-2011-3-0593"
文摘Using multiple stochastic integrals and the stochastic calculus for the frac-tional Brownian sheet, we define and we analyze the 2D-fractional stochastic currents.
