一类新的抛物型变分不等式的随机方法

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2012-03-21 DOI:10.1080/17442508.2014.989396

Tianyang Nie

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引用次数: 10

摘要

我们研究了以下具有两个子微分算子的拟线性偏微分方程:是凸下半连续函数的次微分。．我们定义了这类偏微分方程的黏度解，并证明了不依赖时黏度解的唯一性。为了证明黏度解的存在性，我们将建立一个Feymann-Kac型的随机表示公式。为此，我们研究了一个完全耦合的前向后随机变分不等式。

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A stochastic approach to a new type of parabolic variational inequalities

We study the following quasilinear partial differential equation with two subdifferential operators:where for and The operator (resp. ) is the subdifferential of the convex lower semicontinuous function (resp. ). We define the viscosity solution for such kind of partial differential equation and prove the uniqueness of the viscosity solution when does not depend on . To prove the existence of a viscosity solution, a stochastic representation formula of Feymann–Kac type will be developed. For this end, we investigate a fully coupled forward–backward stochastic variational inequality.

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来源期刊

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.