STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 卷:127 |
Young differential equations with power type nonlinearities | |
Article | |
Leon, Jorge A.1  Nualart, David2  Tindel, Samy3  | |
[1] CINVESTAV IPN, Dept Control Automat, Apartado Postal 14-740, Mexico City 07000, DF, Mexico | |
[2] Univ Kansas, Dept Math, 405 Snow Hall, Lawrence, KS 66045 USA | |
[3] Purdue Univ, Dept Math, 150 N Univ St, W Lafayette, IN 47907 USA | |
关键词: Fractional Brownian motion; Fractional calculus; Young integration; Integral equations; | |
DOI : 10.1016/j.spa.2017.01.007 | |
来源: Elsevier | |
【 摘 要 】
In this note we give several methods to construct nontrivial solutions to the equation d(yt) = sigma(y(t))dx(t) where x is a gamma-Holder R-d-valued signal with gamma is an element of(1/2, 1) and a is a function behaving like a power function |xi|(k), with K is an element of (0, 1). In this situation, classical Young integration techniques allow to get existence and uniqueness results whenever gamma(K + 1) > 1, while we focus on cases where gamma(K + 1) <= 1. Our analysis then relies on Zahle's extension (Zahle, 1998) of Young's integral allowing to cover the situation at hand. (C) 2017 Elsevier B.V. All rights reserved.
【 授权许可】
Free
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
10_1016_j_spa_2017_01_007.pdf | 555KB | download |