• Title/Summary/Keyword: martingle measure

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ON A MARTINGALE PROBLEM AND A RELAXED CONTROL PROBLEM W.R.T. SDE

  • Cho, Nhan-Sook
    • Journal of the Korean Mathematical Society
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    • v.33 no.4
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    • pp.777-791
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    • 1996
  • Let $S(R^d)$ be the Schwartz space of infinitely differentiable functions on $R^d$ which vanish at $\infty$ and $S'(R^d)$ be its dual space. The theory of stochastic differential equations(SDEs) governing processes that takes values in the dual of countably Hilbertian nuclear space such as $S'(R^d)$ studied by many authors(e.g [M],[KM]). Let M be a martingale measure defined by Walsh[W], then M can be considered as a $S'(R^d)$-valued process in a certain condition i.e. M has a version of $S'(R^d)$-valued martingale process. (See [W] for detailed discussion)

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