On stochastics equations with respect to semimartingales ii. itô formula in banach spaces
On stochastics equations with respect to semimartingales ii. itô formula in banach spaces
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DOI：
10.1080/17442508208833202
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发表时间：
1982
期刊：
影响因子：
--
通讯作者：
I. Gyöngy;N. Krylov
中科院分区：
文献类型：
--
作者：
I. Gyöngy;N. Krylov
本文的第二部分在Banach空间中证明了一个一般的Ito公式。一种特殊情况如下。设是一个具有连续稠密注入的空间三元组（V是一个Banach空间，它的对偶是V *，H是一个Hilbert空间）。考虑完备概率空间（Ω，FP）上的V *-值半鞅y，其中V * 是V *-值渐进可测过程，A是实值非减适应cadlag过程，h是H-值局部平方可积鞅。设y = v（直到dP×dA（t）零集），v是v值渐进可测过程，且几乎必然关于dA（t）局部可积.然后，在不可逆性下，y是H-值适应cadlag过程，Ito公式对成立。
In the second part of this study a general Ito formula is proved in Banach spaces. A special case reads as follows. Let be a triple of spaces (V is a Banach space with its dual V *, H is a Hilbert space) with continuous dense injections. Consider a V *-valued semi-martingale y of the form on a complete probability space (Ω,FP) endowed with a filtration where V * is a V *-valued progressively measurable process, A is a real-valued nondecreasing adapted cadlag process and h is an H-valued locally square integrable martingale. Suppose that y = v (up to a dP×dA(t) null-set) for a v-valued progressively measurable process v, and that are almost surely locally integrable with respect to dA(t). Then, up to indistinguishability, y is an H-valued adapted cadlag process and the Ito formula is valid for .