Successive Approximations to Solutions of Stochastic Differential Equations
Successive Approximations to Solutions of Stochastic Differential Equations
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DOI：
10.1016/0022-0396(92)90148-g
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发表时间：
1992-03
影响因子：
2.4
通讯作者：
T. Taniguchi
中科院分区：
文献类型：
--
作者：
T. Taniguchi
本文研究了由逐次逼近法构造的随机过程序列在什么条件下一致收敛于Ito型随机微分方程的解，并在更一般的条件下给出了上述方程解的局部或整体存在唯一性定理。我们注意到本文的引理3是Gard引理的推广，并保证了分别证明了满足定理2和定理3条件的函数的存在性。定理3是Yamada定理的一个推广，它是用逐次逼近法证明的。
In the present paper we shall investigate under what conditions the sequence of stochastic processes constructed by the successive approximations converges uniformly to solutions of a stochastic differential equation of Ito type and shall present the local or global existence and uniqueness theorem for solutions of the above mentioned equation under more general conditions.We note that Lemma 3 in this paper is a generalization of Gard's lemma and guarantees the existence of functions which satisfy the conditions of Theorems 2 and 3 in this paper, respectively. Theorem 3 includes as a special case a generalization of Yamada's theorem which is proved by the method of the successive approximations.