The Doob-Meyer decomposition revisited
The Doob-Meyer decomposition revisited
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DOI：
10.4153/cmb-1996-018-8
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发表时间：
1996-06-01
影响因子：
0.6
通讯作者：
Bass, RF
中科院分区：
文献类型：
--
作者：
Bass, RF
给出了上鞅的Doob-Meyer分解为鞅和降鞅部分的一个新的证明。虽然不是最简洁的证明，但证明是基本的，因为没有比Doob不等式更复杂的证明。如果上鞅是有界的且跳跃时间是完全不可达的，则证明了离散时间逼近收敛于L（2）中的下降部分。一般情况是通过简化为上述特殊情况来处理的。
A new proof is given of the Doob-Meyer decomposition of a supermartingale into martingale and decreasing parts. Although not the most concise proof, the proof is elementary in the sense that nothing more sophisticated than Doob's inequality is used. If the supermartingale is bounded and the jump times are totally inaccessible, then it is shown that discrete time approximations converge to the decreasing part in L(2). The general case is handled by reduction to the above special case.