Communications of the Korean Mathematical Society (대한수학회논문집)
- Volume 10 Issue 1
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- Pages.207-213
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- 1995
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- 1225-1763(pISSN)
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- 2234-3024(eISSN)
RELATIONS BETWEEN THE ITO PROCESSES
Abstract
Let $(\Omega, F, P)$ be a probability space with F a $\sigma$-algebra of subsets of the measure space $\Omega$ and P a probability measure on $\Omega$. Suppose $a > 0$ and let $(F_t)_{t \in [0,a]}$ be an increasing family of sub-$\sigma$-algebras of F. If $r > 0$, let $J = [-r,0]$ and $C(J, R^n)$ the Banach space of all continuous paths $\gamma : J \to R^n$ with the sup-norm $\Vert \gamma \Vert = sup_{s \in J}