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Anticipating Integral Equations
Potential Analysis, 2000The authors consider a stochastic Volterra equation of the form \[ X_t= Y_t+ \int^t_0 F_1(t,s,X_s) ds+\int^t_0 G(t,s)H (s,X_s)dW_s, \] where \(W\) is a real Brownian motion which generates the filtration \({\mathcal F}\), \(H(s,x)\) is a progressively measurable process and \(G(t,s)\) is \({\mathcal F}_t\)-measurable and smooth in Malliavin calculus ...
León, Jorge A., Nualart, David
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Journal of Mathematical Physics, 1966
The integral equation P ∫ cK(ζ′,ζ)ζ′−ζφ(ζ′) dζ′=h(ζ)φ(ζ)+f(ζ)is shown to have simple solutions obtained by standard and elementary methods if h and K have appropriate analytic properties.
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The integral equation P ∫ cK(ζ′,ζ)ζ′−ζφ(ζ′) dζ′=h(ζ)φ(ζ)+f(ζ)is shown to have simple solutions obtained by standard and elementary methods if h and K have appropriate analytic properties.
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1990
Abstract An integral equation is an equation in which an unknown function appears under an integral sign and the problem of solving the equation is to determine that function. As we shall soon see, some problems of mathematical physics lead directly to integral equations, and other problems, which lead first to ordinary or partial ...
David Porter, David S. G. Stirling
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Abstract An integral equation is an equation in which an unknown function appears under an integral sign and the problem of solving the equation is to determine that function. As we shall soon see, some problems of mathematical physics lead directly to integral equations, and other problems, which lead first to ordinary or partial ...
David Porter, David S. G. Stirling
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1991
The paper is a general survey of linear integral equations of all kinds studied till now in the literature, both theoretical and applicative. The general plan of each type presentation is the underlining of its apparition, the general results obtained during its development, the major contributions of the authors working in the domain, the methods used
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The paper is a general survey of linear integral equations of all kinds studied till now in the literature, both theoretical and applicative. The general plan of each type presentation is the underlining of its apparition, the general results obtained during its development, the major contributions of the authors working in the domain, the methods used
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Abel’s Integral Equation and Singular Integral Equations
2011Abel’s integral equation occurs in many branches of scientific fields [1], such as microscopy, seismology, radio astronomy, electron emission, atomic scattering, radar ranging, plasma diagnostics, X-ray radiography, and optical fiber evaluation. Abel’s integral equation is the earliest example of an integral equation [2].
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An overview of real‐world data sources for oncology and considerations for research
Ca-A Cancer Journal for Clinicians, 2022Lynne Penberthy +2 more
exaly