Journal of the Korean Mathematical Society (대한수학회지)
- Volume 33 Issue 4
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- Pages.777-791
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- 1996
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- 0304-9914(pISSN)
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- 2234-3008(eISSN)
ON A MARTINGALE PROBLEM AND A RELAXED CONTROL PROBLEM W.R.T. SDE
Abstract
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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