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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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