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| A Non-Linear Filtering Problem and Its Applications |
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Citation： |
Situ Rong.A Non-Linear Filtering Problem and Its Applications[J].Chinese Annals of Mathematics B,1987,8(3):296~310 |
| Page view： 744
Net amount： 718 |
Authors： |
Situ Rong; |
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| Abstract： |
For partially observed process in n-dimensional space
$\[\left\{ \begin{array}{l}
{\beta _i} = {\beta _0} + \int\limits_0^t {{A_1}(s,{\beta _t})ds + \int\limits_0^t {{B_1}(s,{\beta _s})d{w_s}^{(1)},} } \{\xi _i} = \int\limits_0^t {B(s,{\xi _s}){B^*}(s,{\xi _s})\varphi (s,{\beta _s})ds + \int\limits_0^t {B(s,{\xi _s})d{w_s},} }
\end{array} \right.\]$
under non-Lipschitz (even discontinuous) condition, a Bayes formula different from [1] is derived (Theorem 1). By means of this formula the innovation problem for the above process under rather weak condition is solved (Theorem 2) .Then the existence of an optimal pathwise Bang-Bang control for a partially observed process with bounded controls is obtained (Theorem 4). |
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