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Young differential equations with power type nonlinearities

Author

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  • León, Jorge A.
  • Nualart, David
  • Tindel, Samy

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.

Suggested Citation

  • León, Jorge A. & Nualart, David & Tindel, Samy, 2017. "Young differential equations with power type nonlinearities," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 3042-3067.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:9:p:3042-3067
    DOI: 10.1016/j.spa.2017.01.007
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    Cited by:

    1. Chakraborty, Prakash & Tindel, Samy, 2019. "Rough differential equations with power type nonlinearities," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1533-1555.

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