A New Probabilistic Approach
نویسنده
چکیده
Abstract. Consider the critical measure-valued processX(t, ·) onRd corresponding to the evolution equation ut = ρ(x)1u−u2.We prove that the maximal order of ρ(x) for having the compact support property for X is different for d = 1 and d ≥ 2: it is O(x3) in one dimension and O(x2) in higher dimensions. These growth orders also turn out to be the maximal orders for the nonexistence of a nonnegative nonzero solution for
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