Solving equations with semimartingale noise

IF 0.3 Q4 STATISTICS & PROBABILITY Random Operators and Stochastic Equations Pub Date : 2022-01-23 DOI:10.1515/rose-2021-2070
Jonathan Gutierrez-Pavón, Carlos G. Pacheco
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引用次数: 1

Abstract

Abstract In this work we focus on a method for solving equations with a coefficient formally given in terms of the derivative of a continuous semimartingale. This generalizes the case of coefficients being the white noise. The idea for solving the equation is to find explicitly the inverse of the ill-posed differential operator, which boils down to finding the associated Green kernel. To find the kernel we give explicitly two homogeneous solutions in terms of the so-called Dolean–Dade exponential. The general idea to define rigorously differential operators lies on dealing with them through bilinear forms. We give several examples with explicit calculations.
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求解带有半鞅噪声的方程
摘要在这项工作中,我们重点讨论了一种用连续半鞅的导数形式给出系数的方程组的求解方法。这推广了系数是白噪声的情况。求解方程的想法是明确地找到不适定微分算子的逆,这归结为找到相关的格林核。为了找到核,我们根据所谓的Dolean–Dade指数明确给出了两个齐次解。定义严格微分算子的一般思想在于通过双线性形式处理它们。我们给出了几个带有显式计算的例子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Random Operators and Stochastic Equations
Random Operators and Stochastic Equations STATISTICS & PROBABILITY-
CiteScore
0.60
自引率
25.00%
发文量
24
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