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The arcsine law in the generalized analogue of wiener space
류근식 충청수학회 2017 충청수학회지 Vol.30 No.1
In this note, we prove the theorems in the generalized analogue of Wiener space corresponding to the second and the third arcsine laws in either concrete or analogue of Wiener space [1,2,7] and we show that our results are exactly same to either the concrete or the analogue of Wiener case when the initial condition gives either the Dirac measure at the origin or the probability Borel measure.
THE GENERALIZED FERNIQUE'S THEOREM FOR ANALOGUE OF WIENER MEASURE SPACE
류근식 충청수학회 2009 충청수학회지 Vol.22 No.4
In 1970, Fernique proved that there is a positive realnumber α such that[수식] is finite where (B; P) isan abstract Wiener measure space and [수식] is a measurable normon (B, P) in [2, 3]. In this article, we investigate the existenceof the integral[수식] is theanalogue of Wiener measure space and p and α are both positivereal numbers.
The Dobrakov integral over paths
류근식 충청수학회 2006 충청수학회지 Vol.19 No.1
In 2002, the author introduced the definition and its properties of an analogue of Wiener measure over paths. In this article, using these concepts, we will derive an operator-valued measure over paths and will investigate the properties for integral with respect to the measure. Specially, we will prove the Wiener integral formula for our integral and give some example of it. In 2002, the author introduced the definition and its properties of an analogue of Wiener measure over paths. In this article, using these concepts, we will derive an operator-valued measure over paths and will investigate the properties for integral with respect to the measure. Specially, we will prove the Wiener integral formula for our integral and give some example of it.
The measure-valued Dyson series and its stability theorem
류근식,임만규 대한수학회 2006 대한수학회지 Vol.43 No.3
In this article, we establish the existence theorem for measure-valued Dysonseries and show that it satisfies the Volterra-type integral equation. Furthermore,we prove the stability theorems for measure-valued Dyson series.
THE SIMPLE FORMULA OF CONDITIONAL EXPECTATION ON ANALOGUE OF WIENER MEASURE
류근식 호남수학회 2008 호남수학학술지 Vol.30 No.4
In this note, we establish the uniqueness theorem of conditional expectation on analogue of Wiener measure space for given distributions and prove the simple formula of conditional expectation on analogue of Wiener measure which is essentially similar to Park and Skoug’s formula on the concrete Wiener measure.
The Rotation Theorem on Analogue of Wiener Space
류근식,심성훈 호남수학회 2007 호남수학학술지 Vol.29 No.4
Bearman’s rotation theorem is not only very importantin pure mathematics but also plays the key role for various researchareas, related to Wiener measure. In 2002, the author and professorIm introduced the concept of analogue of Wiener measure, a kindof generalization of Wiener measure and they presented the severalpapers associated with it. In this article, we prove a formula onanalogue of Wiener measure, similar to the formula in Bearman’srotation theorem.
THE GENERALIZED ANALOGUE OF WIENER MEASURE SPACE AND ITS PROPERTIES
류근식 호남수학회 2010 호남수학학술지 Vol.32 No.4
In this note, we introduce the de¯nition of the gener-alized analogue of Wiener measure on the space C[a, b] of all real-valued continuous functions on the closed interval [a, b], give several examples of it and investigate some important properties of it - the Fernique theorem and the existence theorem of scale-invariant mea-surable subsets on C[a, b].
The translation theorem on the generalized analogue of Wiener space and its applications
류근식 충청수학회 2013 충청수학회지 Vol.26 No.4
In this note, we prove the translation theorem for the generalized analogue of Wiener measure space and we show some properties of the generalized analogue of Wiener measure from it.
FGK INEQUALITY ON THE ANALOGUE OF WIENER SPACE
류근식 호남수학회 2012 호남수학학술지 Vol.34 No.2
This work aims at proving the FKG inequalities for the analogue of Wiener functionals with special orders on the analogue of Wiener space.