Abstract
Under the condition of arc-wise smooth path of integration§the Plemelj formula of Cauchy-type integral on random process with second order moment is obtained.
Highlights
Let L be a simple, smooth and closed curve. It divides the complex plan into inter domain D+ and outer domain D−. (Ω, F, P) is a probability space, g(ω, ζ) is a random process with second order moment on (Ω, F, P), which depends on parameters ζ on L
In [Wang, 2004], Wang Chuangrong gave the definition of random cauchy-type integral of g(ω, ζ), and proved the existence of random singular integral on arc-wise smooth curve L
In [Wang, 2005], the author discussed some properties of random singular integral, proved that random singular integral operator was a linear bounded operator and gave the plemelj fomula of random cauchy-type integral on smooth curve L
Summary
Let L be a simple, smooth and closed curve. It divides the complex plan into inter domain D+ and outer domain D−. (Ω, F, P) is a probability space, g(ω, ζ) is a random process with second order moment on (Ω, F, P), which depends on parameters ζ on L. Plemelj Formula of Cauchy-Type Integral of Random Process with Second Order Moment Feng Lin School of mathematics, Huaqiao University Cun Yao School of mathematics, Huaqiao University
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