On the Martingale Problem for Measure-Valued Markov Branching Processes
On the Martingale Problem for Measure-Valued Markov Branching Processes
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DOI：
10.1007/978-1-4612-0381-0_4
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
P. Fitzsimmons
中科院分区：
文献类型：
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作者：
P. Fitzsimmons
用[F]中的定理（4.1）(b)说明了与（ξ， ø）- superprocessx相关的鞅问题具有唯一解。定理是正确的，但[F]中提供的证明是不充分的，因为p. 355上t→Vtf(x)连续可微的断言一般是错误的。我们在这篇笔记中的目的是给出这个结果的一个完整的证明。由于在[F]中使用的假设的弱点，证明相当复杂，但由于该定理最近得到了应用（例如[DP]），我们认为有必要进行彻底的处理。此外，关于时空鞅的主要辅助结果（定理（2.22））可能具有独立的兴趣。在本节的剩余部分，我们回顾[F]中的一些符号，并陈述正在讨论的定理。所有未解释的符号如[F]所示。
It was stated as Theorem (4.1)(b) in [F] that the martingale problem associated with the (ξ, ø)-superprocessXdiscussed in that paper has a unique solution. The theorem is true, but the proof supplied in [F] is inadequate since the assertion on p. 355 thatt→Vtf(x) is continuously differentiable is false in general. Our purpose in this note is to give a complete proof of this result. Owing to the weakness of the hypotheses employed in [F], the proof is rather involved, but since the theorem has found recent application (e.g. [DP]), we thought a thorough treatment was warranted. Also, the main auxiliary result (Theorem (2.22)) concerning space-time martingales may be of independent interest. In the remainder of this section we recall some notation from [F] and state the theorem under discussion. All unexplained notation is as in [F].