Rough differential equations with power type nonlinearities

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Chakraborty, Prakash¹  Tindel, Samy² 

[1] Purdue Univ, Dept Stat, 150 N Univ St, W Lafayette, IN 47907 USA

[2] Purdue Univ, Dept Math, 150 N Univ St, W Lafayette, IN 47907 USA

关键词: Rough path;    Rough differential equation;   

DOI  :  10.1016/j.spa.2018.05.010

来源: Elsevier

【 摘 要 】

In this note we consider differential equations driven by a signal x which is gamma-Holder with gamma > 1/3 and is assumed to possess a lift as a rough path. Our main point is to obtain existence of solutions when the coefficients of the equation behave like power functions of the form vertical bar xi vertical bar(kappa) with kappa epsilon (0, 1). Two different methods are used in order to construct solutions: (i) In a 1-d setting, we resort to a rough version of Lamperti's transform. (ii) For multidimensional situations, we quantify some improved regularity estimates when the solution approaches the origin. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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