TY - JOUR
T1 - SPDEs with rough noise in space: Hölder continuity of the solution
AU - Balan, Raluca M.
AU - Jolis, Maria
AU - Quer-Sardanyons, Lluís
PY - 2016/12/1
Y1 - 2016/12/1
N2 - © 2016 Elsevier B.V. We consider the stochastic wave and heat equations with affine multiplicative Gaussian noise which is white in time and behaves in space like the fractional Brownian motion with index H∈(14,12). The existence and uniqueness of the solution to these equations has been proved recently by the authors. In the present note we show that these solutions have modifications which are Hölder continuous in space of order smaller than H, and Hölder continuous in time of order smaller than γ, where γ=H for the wave equation and γ=H/2 for the heat equation.
AB - © 2016 Elsevier B.V. We consider the stochastic wave and heat equations with affine multiplicative Gaussian noise which is white in time and behaves in space like the fractional Brownian motion with index H∈(14,12). The existence and uniqueness of the solution to these equations has been proved recently by the authors. In the present note we show that these solutions have modifications which are Hölder continuous in space of order smaller than H, and Hölder continuous in time of order smaller than γ, where γ=H for the wave equation and γ=H/2 for the heat equation.
KW - Fractional noise
KW - Hölder continuous paths
KW - Stochastic heat equation
KW - Stochastic wave equation
U2 - 10.1016/j.spl.2016.09.003
DO - 10.1016/j.spl.2016.09.003
M3 - Article
SN - 0167-7152
VL - 119
SP - 310
EP - 316
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
ER -