共查询到7条相似文献,搜索用时 0 毫秒
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Dapeng Zhan 《Stochastic Processes and their Applications》2019,129(1):129-152
We show that, for , the integral of the laws of two-sided radial SLE curves through different interior points against a measure with SLE Green’s function density is the law of a chordal SLE curve, biased by the path’s natural length. We also show that, for , the integral of the laws of extended SLE curves through different interior points against a measure with a closed formula density restricted in a bounded set is the law of a chordal SLE curve, biased by the path’s capacity length restricted in that set. Another result is that, for , if one integrates the laws of two-sided chordal SLE curves through different force points on against a measure with density on , then one also gets a law that is absolutely continuous w.r.t. that of a chordal SLE curve. To obtain these results, we develop a framework to study stochastic processes with random lifetime, and improve the traditional Girsanov’s Theorem. 相似文献
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Gelfand–Shilov spaces are spaces of entire functions defined in terms of a rate of growth in one direction and a concomitant rate of decay in an orthogonal direction. Gelfand and Shilov proved that the Fourier transform is an isomorphism among certain of these spaces. In this article we consider mapping properties of fractional Fourier transforms on Gelfand–Shilov spaces. Just as the Fourier transform corresponds to rotation through a right angle in the phase plane, fractional Fourier transforms correspond to rotations through intermediate angles. Therefore, the aim of fractional Fourier estimates is to set up a correspondence between growth properties in the complex plane versus decay properties in phase space. 相似文献
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A. J. B. Ward 《International Journal of Mathematical Education in Science & Technology》2013,44(1):158-160
A simple method for teaching the algebraic solution of cubic equations is presented. The approach is via ‘completion of the cube’. It is found that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. Many people are surprised at how simple the algebraic solution of cubic equations turns out to be. It is not normally necessary to resort to numerical techniques for these equations. 相似文献
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