The Simple Formula of Conditional Expectation on Analogue of Wiener Measure

Ryu, Kun-Sik

doi:10.5831/hmj.2008.30.4.723

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The Simple Formula For Conditional Expectation On Analogue O2

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Cited by 3 publications

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“…In 2008, Professor D. H. Cho proved the next theorem by the quite different and long method on the analogue of Wiener space over paths in B [8], compare with our proof in [35]. Fðy À ½y þ ½ũ uÞdm ' ðyÞ dP ' Jt t ðũ uÞ…”

Section: The Simple Formula For Conditional Expectation On Analogue Omentioning

confidence: 59%

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Survey of the Theories for Analogue of Wiener Measure Space

Ryu¹,

Im²,

Choi

2009

IIS

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We consider the analogue of Wiener measure on the space of all real continuous functions, and then establish the measure-valued measure and the operator-valued measure on our space and we investigate their important properties, for example, the integration formula, the rotation theorem, the Bartle integral, the Bochner integral and the Dobrakov integral, the simple formula for conditional expectation, the measure-valued Feynman-Kac formula and Volterra integral equation and integral transform.

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Section: The Simple Formula For Conditional Expectation On Analogue Omentioning

confidence: 59%

“…; u n Þ in R nþ1 . By [35], we have following theorem from the direct calculations Eðexpfi 1 X þ i 2 YgÞ ¼ Eðexpfi 1 XgÞ Eðexpfi 2 YgÞ and Eðexpfi 1 X þ i 3 ZgÞ ¼ Eðexpfi 1 XgÞ Eðexpfi 3 ZgÞ.…”

Section: The Simple Formula For Conditional Expectation On Analogue Omentioning

confidence: 99%