Mean-Square Exponential Input-to-State Stability of Stochastic Fuzzy Recurrent Neural Networks with Multiproportional Delays and Distributed Delays

We are interested in a class of stochastic fuzzy recurrent neural networks with multiproportional delays and distributed delays. By constructing suitable Lyapunov-Krasovskii functionals and applying stochastic analysis theory, Ito^’s formula and Dynkin’s formula, we derive novel sufficient conditions for mean-square exponential input-to-state stability of the suggested system. Some remarks and discussions are given to show that our results extend and improve some previous results in the literature. Finally, two examples and their simulations are provided to illustrate the effectiveness of the theoretical results.

FIRST PASSAGE TIMES OF REFLECTED GENERALIZED ORNSTEIN–UHLENBECK PROCESSES

We study first passage problems of a class of reflected generalized Ornstein–Uhlenbeck processes without positive jumps. By establishing an extended Dynkin's formula associated with the process, we derive that the joint Laplace transform of the first passage time and an integral functional stopped at the time satisfies a truncated integro-differential equation. Two solvable examples are presented when the driven Lévy process is a drifted-Brownian motion and a spectrally negative stable process with index α ∈ (1, 2], respectively. Finally, we give two applications in finance.