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Random Variables01:09

Random Variables

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A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
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Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Random Error01:04

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Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
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Random and Systematic Errors01:20

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Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...
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Neural Regulation01:37

Neural Regulation

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Digestion begins with a cephalic phase that prepares the digestive system to receive food. When our brain processes visual or olfactory information about food, it triggers impulses in the cranial nerves innervating the salivary glands and stomach to prepare for food.
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Probability Distributions01:32

Probability Distributions

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 The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
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随机神经网络用于大致波动.

Antoine Jacquier1,2, Žan Žurič1

  • 1Department of Mathematics, Imperial College London, London, UK.

Applied mathematics and optimization
|March 10, 2026
PubMed
概括
此摘要是机器生成的。

我们开发了一个深度学习算法来解决复杂的金融数学问题. 这种新的储存神经网络方法为粗略的波动性建模提供了强大而理论上健全的方法.

关键词:
神经网络的神经网络的神经网络储水库计算器 储水库计算粗暴的波动性 粗暴的波动性特别专项教育项目 (SPDEs)

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科学领域:

  • 量化金融 量化金融
  • 计算数学 计算数学 计算数学
  • 机器学习 机器学习

背景情况:

  • 路径依赖的部分微分方程 (PDEs) 在金融建模中至关重要,特别是对于粗略波动.
  • 通过分析来解决这些复杂的方程往往是难以解决的.
  • 现有的数值方法可能会面临高维度和粗略波动动态的挑战.

研究的目的:

  • 开发一种基于深度学习的新型数值算法,用于在粗略的波动性建模中解决路径依赖的PDEs.
  • 利用最近在随机微分方程和神经网络架构方面的进展.
  • 提供理论上有基础的,计算上高效的解决方案.

主要方法:

  • 解释部分微分方程 (PDE) 作为一个逆向随机微分方程 (BSDE) 的解.
  • 使用一种水库类型的神经网络架构,灵感来自Gonon,Grigoryeva和Ortega.
  • 将优化问题用简单的最小平方回归来表达.

主要成果:

  • 提出的深度学习算法有效地解决了与粗波动相关的路径依赖的PDEs.
  • 储库神经网络方法简化了对最小平方回归问题的优化.
  • 对于这个问题,我们建立了储库方法的理论收性质.

结论:

  • 深度学习,特别是储备神经网络,为解决复杂的金融PDE提供了强大的工具.
  • 与水库网络相结合的BSDE解释提供了一种融合且高效的数值方法.
  • 这种方法推进了用于粗略波动性建模的可用的计算技术.