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Stability for generalized stochastic equations

Author

Listed:
  • Andrade da Silva, F.
  • Bonotto, E.M.
  • Federson, M.

Abstract

Similarly to generalized ordinary differential equations that comprise various types of classical deterministic equations, generalized stochastic equations (GSEs) were created to contain equations involving stochastic processes. The main goal of this paper is to investigate several types of stability and boundedness for non-autonomous GSEs by means of Lyapunov functionals. We also established existence–uniqueness results for maximal and global forward solutions of GSEs and applied our result to the Ornstein–Uhlenbeck process.

Suggested Citation

  • Andrade da Silva, F. & Bonotto, E.M. & Federson, M., 2024. "Stability for generalized stochastic equations," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    • Handle: RePEc:eee:spapps:v:173:y:2024:i:c:s0304414924000644
    DOI: 10.1016/j.spa.2024.104358
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    References listed on IDEAS

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    1. M. Federson & R. Grau & J. G. Mesquita, 2019. "Prolongation of solutions of measure differential equations and dynamic equations on time scales," Mathematische Nachrichten, Wiley Blackwell, vol. 292(1), pages 22-55, January.
    2. Márcia Federson & Jaqueline G. Mesquita & Eduard Toon, 2015. "Lyapunov theorems for measure functional differential equations via Kurzweil-equations," Mathematische Nachrichten, Wiley Blackwell, vol. 288(13), pages 1487-1511, September.
    3. Rainer Schöbel & Jianwei Zhu, 1999. "Stochastic Volatility With an Ornstein–Uhlenbeck Process: An Extension," Review of Finance, European Finance Association, vol. 3(1), pages 23-46.
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