Almost-sure Explosive Solutions of Some Nonlinear Parabolic Itô Equations

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【作者】 Pao-Liu Chow 

【摘要】The paper is concerned with the problem of explosive solutions to a class of nonlinear parabolic Itô equations. Under some sufficient conditions on the initial state and the nonlinear coefficients; it will be shown that the solutions will explode in finite time almost surely. Theorem 3.1 is concerned with the existence of a unique local strong solution. The main result is presented in Theorem 3.2. With the aid of Lemma 3.3 and Lemma 3.4; this theorem is proved by adopting the method of auxiliary functionals combined with the method of cycles. An example is given to illustrate the application of the main theorem.