Given a stochastic differential equation with path-dependent coefficients driven by a multidimensional Wiener process, we show that the support of the law of the solution is given by the image of the Cameron-Martin space under the flow of the solutions of a system of path-dependent (ordinary) differential equations. Our result extends the Stroock-Varadhan support theorem for diffusion processes to the case of SDEs with path-dependent coefficients. The proof is based on the Functional Ito calculus and interpolation estimates for stochastic processes in Holder norm.

中文翻译：

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关于具有路径相关系数的随机微分方程解的支持

给定一个由多维维纳过程驱动的具有路径相关系数的随机微分方程，我们证明了解律的支持是由卡梅伦-马丁空间在路径系统的解流动下的图像给出的依赖（常）微分方程。我们的结果将扩散过程的 Stroock-Varadhan 支持定理扩展到具有路径相关系数的 SDE 的情况。该证明基于Holder 范数中随机过程的泛函Ito 演算和插值估计。