Rough differential equations with power type nonlinearities

Prakash Chakraborty and Samy Tindel

Stochastic Processes and their Applications, 2019, vol. 129, issue 5, 1533-1555

Abstract: In this note we consider differential equations driven by a signal x which is γ-Hölder with γ>13, 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 |ξ|κ with κ∈(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.

Keywords: Rough path; Rough differential equation (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spa.2018.05.010

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