The Rotation Theorem on Analogue of Wiener Space

Ryu, Kun-Sik; Shim, Shung-Hoon

doi:10.5831/hmj.2007.29.4.577

Cited by 3 publications

(2 citation statements)

References 6 publications

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“…In [18,19], the authors introduced an analogue of the Wiener measure w ϕ on (C[0, T ], B(C[0, T ])), using a probability measure ϕ on (R, B(R)). Furthermore, in [5,6,17,20], the authors studied various topics pertaining to this analogue of the Wiener measure, together with related topics concerning an analogue of Wiener space. In particular, the authors derived a simple formula for the conditional w ϕ -integral and then used this formula to evaluate the conditional w ϕ -integral of various functionals [3,16].…”

Section: Introductionmentioning

confidence: 99%

Applications of an analogue of conditional Wiener integrals

Lee¹,

Chung²,

Chang³

2015

Ann. Funct. Anal.

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Section: Introductionmentioning

confidence: 99%

Applications of an analogue of conditional Wiener integrals

Lee¹,

Chung²,

Chang³

2015

Ann. Funct. Anal.

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“…In 2002, the author and Professor Im defined the analogue of Wiener measure ω ϕ on the space C [a, b], the space of all real-valued continuous functions on [a, b], associated with a complex Borel measure ϕ on R [5,14,15,16]. Indeed, if we take ϕ = δ 0 , the Dirac measure at the origin 0 in R, ω ϕ is the concrete Wiener measure m w .…”

Section: Introductionmentioning

confidence: 99%

Integration With Respect to Analogue of Wiener Measure Over Paths in Wiener Space and Its Applications

Ryu¹

2010

Bulletin of the Korean Mathematical Society

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Abstract. In 1992, the author introduced the definition and the properties of Wiener measure over paths in abstract Wiener space and this measure was investigated extensively by some mathematicians. In 2002, the author and Dr. Im presented an article for analogue of Wiener measure and its applications which is the generalized theory of Wiener measure theory. In this note, we will derive the analogue of Wiener measure over paths in abstract Wiener space and establish two integration formulae, one is similar to the Wiener integration formula and another is similar to simple formula for conditional Wiener integral. Furthermore, we will give some examples for our formulae.

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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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The Rotation Theorem on Analogue of Wiener Space

Cited by 3 publications

References 6 publications

Applications of an analogue of conditional Wiener integrals

Applications of an analogue of conditional Wiener integrals

Integration With Respect to Analogue of Wiener Measure Over Paths in Wiener Space and Its Applications

Survey of the Theories for Analogue of Wiener Measure Space

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