任意阶广义非局部概率
General Nonlocal Probability of Arbitrary Order.
作者信息
Tarasov Vasily E
机构信息
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, Russia.
Department of Physics, 915, Moscow Aviation Institute (National Research University), Moscow 125993, Russia.
出版信息
Entropy (Basel). 2023 Jun 10;25(6):919. doi: 10.3390/e25060919.
Using the Luchko's general fractional calculus (GFC) and its extension in the form of the multi-kernel general fractional calculus of arbitrary order (GFC of AO), a nonlocal generalization of probability is suggested. The nonlocal and general fractional (CF) extensions of probability density functions (PDFs), cumulative distribution functions (CDFs) and probability are defined and its properties are described. Examples of general nonlocal probability distributions of AO are considered. An application of the multi-kernel GFC allows us to consider a wider class of operator kernels and a wider class of nonlocality in the probability theory.
利用卢奇科的广义分数阶微积分（GFC）及其以任意阶多核广义分数阶微积分（AO的GFC）形式的扩展，提出了概率的非局部推广。定义了概率密度函数（PDF）、累积分布函数（CDF）和概率的非局部和广义分数阶（CF）扩展，并描述了其性质。考虑了AO的一般非局部概率分布的示例。多核GFC的应用使我们能够在概率论中考虑更广泛的算子核类和更广泛的非局部性类。
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