“…This property is related the moment bounds of the solution. When (1.1) is parabolic Anderson model, namely, when L is a heat operator or fractional heat operator, then the sharp (both lower and upper) moment bounds are known, see [2,6,5,7,8,17,19,25], and we also refer to [15] and references therein. However, when L is wave operators (namely the hyperbolic Anderson model) or when L is (temporal) fractional differential operators, the situation is different and as far as we know here are the progress achieved.…”