Results 21 to 30 of about 35 (35)
A change of scale formula for Wiener integrals of cylinder functions on the abstract Wiener space II
International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 4, Page 231-237, 2001., 2001 We show that for certain bounded cylinder functions of the form F(x)=μˆ((h1,x)∼,…,(hn,x)∼), x ∈ B where μˆ:ℝn→ℂ is the Fourier‐transform of the complex‐valued Borel measure μ on ℬ(ℝn), the Borel σ‐algebra of ℝn with ‖μ‖ < ∞, the analytic Feynman integral of F exists, although the analytic Feynman integral, limz→−iqIaw(F;z)=limz→−iq(z/2π) n/2∫ℝnf(u→)exp{
Young Sik Kim
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Conditional generalized analytic Feynman integrals and a generalized integral equation
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 11, Page 759-776, 2000., 2000 We use a generalized Brownian motion process to define a generalized Feynman integral and a conditional generalized Feynman integral. We then establish the existence of these integrals for various functionals. Finally we use the conditional generalized Feynman integral to derive a Schrödinger integral equation.
Seung Jun Chang +2 more
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Relationships among transforms, convolutions, and first variations
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 1, Page 191-204, 1999., 1999 In this paper, we establish several interesting relationships involving the Fourier‐Feynman transform, the convolution product, and the first variation for functionals F on Wiener space of the form where 〈αj, x〉 denotes the Paley‐Wiener‐Zygmund stochastic integral .
Jeong Gyoo Kim +3 more
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Infant Mental Health Journal: Infancy and Early Childhood, Volume 46, Issue 1, Page 95-111, January 2025.Abstract We compared referrals and connection to care between perinatal patients: 90 receiving OB/GYN care in clinics with integrated behavioral health consultants with infant mental health specialization (IMH‐BHC), and 68 receiving traditional care, in the United States.
Jennifer M. Jester +8 more
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A change of scale formula for Wiener integrals of cylinder functions on abstract Wiener space
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 1, Page 73-78, 1998., 1996 The purpose of this paper is to establish the existence of analytic Wiener and Feynman integrals for a class of certain cylinder functions which is of the form: on the abstract Wiener space, and to establish the relationship between the Wiener integral and the analytic Feynman integral for such cylinder functions on the abstract Wiener space.
Young Sik Kim
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Journal of Flood Risk Management, Volume 17, Issue 2, June 2024.Abstract Floods are the most frequent types of natural disasters. From the perspective of disaster management, indicators associated with floods are important for accurate flood risk assessment. However, the application of all indicators related to flood risk assessment decreases the evaluation efficiency, because the definitions of the indicators may ...
Hongjun Joo, Wonyoung Choi, Chansoo Jeon
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Generalized transforms and convolutions
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 1, Page 19-32, 1997., 1995 In this paper, using the concept of a generalized Feynman integral, we define a generalized Fourier‐Feynman transform and a generalized convolution product. Then for two classes of functionals on Wiener space we obtain several results involving and relating these generalized transforms and convolutions.
Timothy Huffman, Chull Park, David Skoug
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A change of scale formula for Wiener integrals on abstract Wiener spaces
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 2, Page 239-247, 1994., 1994 In this paper we obtain a change of scale formula for Wiener integrals on abstract Wiener spaces. This formula is shown to hold for many classes of functions of interest in Feynman integration theory and quantum mechanics.
Il Yoo, David Skoug
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Fundamental theorem of Wiener calculus
International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 3, Page 443-452, 1990., 1990 In this paper we define and develop a theory of differentiation in Wiener space C[0, T]. We then proceed to establish a fundamental theorem of the integral calculus for C[0, T]. First of all, we show that the derivative of the indefinite Wiener integral exists and equals the integrand functional.
Chull Park +2 more
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Fourier-Feynman transforms of unbounded functionals on abstract Wiener space
Open Mathematics, 2010 Kim Byoung, Yoo Il, Cho Dong
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