扩散的有限、可积和有界时间嵌入
Finite, integrable and bounded time embeddings for diffusions
摘要：
我们解决了一般时间均匀扩散$X$的Skorokhod嵌入问题（SEP）：给定一个分布$ρ$，我们构造一个停时$τ$，使得停止过程$X_τ$具有分布$ρ$。我们的解决方案的方法利用鞅表示（以类似的方式，以巴斯（在研讨会上的概率XVII。数学讲义784（1983）221-224 Springer），他求解了布朗运动的SEP），并利用了随机微分方程的弱解的唯一性定律。然后，我们问是否存在的SEP分别是有限的几乎必然，可积或有界的解决方案，当我们提出的建设有这些性质。我们提供的条件，保证存在的有限时间的解决方案。然后，我们充分的特点，可以嵌入可积停时的分布。最后，我们得到必要的，充分的，条件下存在一个有界嵌入。
英文摘要：
We solve the Skorokhod embedding problem (SEP) for a general time-homogeneous diffusion $X$: given a distribution $ρ$, we construct a stopping time $τ$ such that the stopped process $X_τ$ has the distribution $ρ$. Our solution method makes use of martingale representations (in a similar way to Bass (In Seminar on Probability XVII. Lecture Notes in Math. 784 (1983) 221-224 Springer) who solves the SEP for Brownian motion) and draws on law uniqueness of weak solutions of SDEs. Then we ask if there exist solutions of the SEP which are respectively finite almost surely, integrable or bounded, and when does our proposed construction have these properties. We provide conditions that guarantee existence of finite time solutions. Then, we fully characterize the distributions that can be embedded with integrable stopping times. Finally, we derive necessary, respectively sufficient, conditions under which there exists a bounded embedding.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
