Young differential equations with power type nonlinearities

Jorge A. León, David Nualart and Samy Tindel

Stochastic Processes and their Applications, 2017, vol. 127, issue 9, 3042-3067

Abstract: In this note we give several methods to construct nontrivial solutions to the equation dyt=σ(yt)dxt, where x is a γ-Hölder Rd-valued signal with γ∈(1/2,1) and σ is a function behaving like a power function |ξ|κ, with κ∈(0,1). In this situation, classical Young integration techniques allow to get existence and uniqueness results whenever γ(κ+1)>1, while we focus on cases where γ(κ+1)≤1. Our analysis then relies on Zähle’s extension (Zähle, 1998) of Young’s integral allowing to cover the situation at hand.

Keywords: Fractional Brownian motion; Fractional calculus; Young integration; Integral equations (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2017.01.007

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