Stability for generalized stochastic equations

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 stabilit...

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Bibliographic Details
Published in:	Stochastic processes and their applications Vol. 173; p. 104358
Main Authors:	Andrade da Silva, F., Bonotto, E.M., Federson, M.
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01-07-2024
Subjects:	Existence and uniqueness of solutions Itô–Henstock integral Kurzweil integral Stability theory for stochastic differential equations Stochastic differential equations Itô–Henstock integral Stochastic differential equations 34G20 60H20 34A12 37H10 Kurzweil integral Stability theory for stochastic differential equations 93D05 93E15 Existence and uniqueness of solutions 26A39 45N99
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Summary:	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.
ISSN:	0304-4149 1879-209X
DOI:	10.1016/j.spa.2024.104358