대한수학회논문집 (Communications of the Korean Mathematical Society)
- 제11권2호
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- Pages.471-480
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- 1996
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- 1225-1763(pISSN)
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- 2234-3024(eISSN)
Twisted product representation of reflected brownian motion in a cone
초록
Consider a strong Markov process $X^0$ that has continuous sample paths in the closed cone $\bar{G}$ in $R^d(d \geq 3)$ such that the process behaves like a ordinary Brownian motion in the interior of the cone, reflects instantaneously from the boundary of the cone and is absorbed at the vertex of the cone. It is shown that $X^0(t)$ has a representation $R(t) \ominus (t)$ where $R(t) \in [0, \infty)$ and $\ominus(t) \in S^{d-1}$, the surface of the unit ball.