具有广义漂移和非光滑色散函数的随机积分方程的路径可解性

IF 1.2 2区数学 Q2 STATISTICS & PROBABILITY Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2013-12-27 DOI:10.1214/14-AIHP660

I. Karatzas, J. Ruf

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引用次数: 6

摘要

我们研究了具有非光滑色散系数和漂移分量的一维随机积分方程，这些漂移分量不受勒贝格测度的绝对连续限制。本着Lamperti, Doss和Sussmann的精神，我们将这些方程的解与某些普通积分方程的解联系起来，这些方程的解由底层概率空间的一般元素表示。这种关系使我们能够在路径意义上求解随机积分方程。

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PATHWISE SOLVABILITY OF STOCHASTIC INTEGRAL EQUATIONS WITH GENERALIZED DRIFT AND NON-SMOOTH DISPERSION FUNCTIONS

We study one-dimensional stochastic integral equations with non-smooth dispersion coefficients, and with drift components that are not restricted to be absolutely continuous with respect to Lebesgue measure. In the spirit of Lamperti, Doss and Sussmann, we relate solutions of such equations to solutions of certain ordinary integral equations, indexed by a generic element of the underlying probability space. This relation allows us to solve the stochastic integral equations in a pathwise sense.

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来源期刊

Annales De L Institut Henri Poincare-probabilites Et Statistiques 数学-统计学与概率论

CiteScore

2.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Probability and Statistics section of the Annales de l’Institut Henri Poincaré is an international journal which publishes high quality research papers. The journal deals with all aspects of modern probability theory and mathematical statistics, as well as with their applications.