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In this paper we study the random approximate travelling wave solutions of the stochastic KPP equations. Two new properties of the stochastic KPP equations are obtained. We prove the ergodicity that for almost all sample paths, behind the wavefront x = γ t, the lower limit of 1 t t 0 u(s, x) ds as t → ∞ is positive, and ahead of the wavefront, the limit is zero. In some cases, behind the wavefront, the limit of 1 t t 0 u(s, x) ds as t → ∞ exists and is positive almost surely. We also prove thatdoi:10.1088/0951-7715/14/3/311 fatcat:hmvnzh6pjvfjbcgo6kre5wv3sy