Results 11 to 20 of about 3,501 (264)
Mathematics, 2020 We prove that the Wiener integral, the analytic Wiener integral and the analytic Feynman integral of the first variation of F(x)=exp{∫0Tθ(t,x(t))dt} successfully exist under the certain condition, where θ(t,u)=∫Rexp{iuv}dσt(v) is a Fourier–Stieltjes ...
Young Sik Kim
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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, 1998 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: F(x)=f((h1,x)∼,⋯,(hn,x)∼), x∈B, on the abstract Wiener space, and to establish the ...
Young Sik Kim
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A Partial Derivative Approach to the Change of Scale Formula for the Function Space Integral
Entropy, 2020 We investigate the partial derivative approach to the change of scale formula for the functon space integral and we investigate the vector calculus approach to the directional derivative on the function space and prove relationships among the Wiener ...
Young Sik Kim
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A change of scale formula for Wiener integrals on abstract Wiener spaces
International Journal of Mathematics and Mathematical Sciences, 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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Wiener Functionals as Itô Integrals [PDF]
The Annals of Probability, 1977 Let W(t, ω) be a standard Wiener process, W t ≡ W(t) ≡ W(t, ∙). A function φ(t, ω) is called nonanticipating iff for all t ^ 0, φ(t, ∙) is measurable with respect to {W s : 0 % s % t}. The Ito stochastic integral $$f(\omega )\, \equiv \,\int {_0^1 \varphi (t,\,\omega )d_t \,W(t,\,\omega )}$$ is defined for any jointly measurable, nonanticipating ...
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Fundamental theorem of Wiener calculus
International Journal of Mathematics and Mathematical Sciences, 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].
Chull Park +2 more
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An Operator-Valued Yeh-Wiener Integral and a Kac-Feynman Wiener Integral Equation [PDF]
Proceedings of the American Mathematical Society, 1994 Let C [ 0 , T ] C[0,T] denote Wiener space, i.e., the space of all continuous functions η ( t ) \eta (t) on [ 0 , T ] [0,T] such that η ( 0 ) = 0
Park, Chull, Skoug, David
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Journal of Function Spaces, 2016 Using simple formulas for generalized conditional Wiener integrals on a function space which is an analogue of Wiener space, we evaluate two generalized analytic conditional Wiener integrals of a generalized cylinder function which is useful in Feynman ...
Dong Hyun Cho
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Generalized Conditional Yeh-Wiener Integrals and a Wiener Interal Equation
Journal of Integral Equations and Applications, 1993 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Park, Chull, Skoug, David
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On Determinant Expansions for Hankel Operators
Concrete Operators, 2020 Let w be a semiclassical weight that is generic in Magnus’s sense, and (pn)n=0∞({p_n})_{n = 0}^\infty the corresponding sequence of orthogonal polynomials. We express the Christoffel–Darboux kernel as a sum of products of Hankel integral operators.
Blower Gordon, Chen Yang
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