A Peano-Like Theorem for Stochastic Differential Equations with Nonlocal Sample Dependence
A Peano-Like Theorem for Stochastic Differential Equations with Nonlocal Sample Dependence
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DOI：
10.1080/07362994.2012.727142
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发表时间：
2013-01
影响因子：
1.3
通讯作者：
P. Kloeden;Thomas Lorenz
中科院分区：
文献类型：
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作者：
P. Kloeden;Thomas Lorenz
具有非局部样本相关性的随机微分方程的不一定唯一强解的存在性是在系数除了连续性之外还满足渐近局部有界条件的假设下建立的。证明是通过类似欧拉的近似构造来实现的。这些方程包括平均场随机微分方程，但非局部样本依赖性可能比仅对解的矩的依赖性更普遍。
The existence of a not-necessarily-unique strong solution for a stochastic differential equations with nonlocal sample dependence is established under the assumption that the coefficients satisfy an asymptotically local boundedness condition in addition to continuity. The proof is by an Euler-like construction of approximations. These equations include mean-field stochastic differential equations, but the nonlocal sample dependence can be more general than just the dependence on moments of the solution.