Define on \(\mathbb{R}^d\) the normalized Gaussian measure\[ d \gamma(x)=\frac{1}{(2\pi)^{\frac{d}{2}}} e^{-\frac{|x|^2}{2}}dx\] Consider first the case \(d= 1\). The Taylor expansion of \(e^{-\frac{1}{2}x^2}\) at the point \(x\), with increment \(t\…
http://blog.csdn.net/pipisorry/article/details/49366047 Hermite埃尔米特多项式 在数学中,埃尔米特多项式是一种经典的正交多项式族,得名于法国数学家夏尔·埃尔米特.概率论里的埃奇沃斯级数的表达式中就要用到埃尔米特多项式.在组合数学中,埃尔米特多项式是阿佩尔方程的解.物理学中,埃尔米特多项式给出了量子谐振子的本征态. 前4个(概率论中的)埃尔米特多项式的图像 The Hermite polynomials are set of ortho…
原文 Hermite Curve Interpolation Hermite Curve Interpolation Hamburg (Germany), the 30th March 1998. Written by Nils Pipenbrinck aka Submissive/Cubic & $eeN Introduction Hermite curves are very easy to calculate but also very powerful. They are used to…
Let \(\partial_i =\frac{\partial}{\partial x_i}\). The operator \(\partial_i\) is unbounded on \(L^2(\gamma)\). We will explore its adjoint operator \(\partial^*_i\) in \(L^2(\gamma)\). For this purpose, take \(f,g\in C_0^{\infty}\), i.e., infinitel…
随机偏微分方程 Throughout this section, let $(\Omega, \calF, \calF_t,\ P)$ be a complete filtered probability space satisfying the usual conditions. 1. Recall the following results: a) The Doob maximal inequality: if $(N_t)$ is a non-negative $\calF…
UNDERSTANDING THE GAUSSIAN DISTRIBUTION Randomness is so present in our reality that we are used to take it for granted. Most of the phenomena which surround us have been generated by random processes. Hence, our brain is very good at recognise these…
题目链接:https://www.patest.cn/contests/pat-a-practise/1002 原题如下: This time, you are supposed to find A+B where A and B are two polynomials. Input Each input file contains one test case. Each case occupies 2 lines, and each line contains the information…
