Traditional finite-time convergence theory for numerical methods applied to stochastic differential equations (SDEs) requires a global Lipschitz assumption on the drift and diffusion coefficients. In practice, many important SDE models satisfy only a local Lipschitz property and, since Brownian paths can make arbitrarily large excursions, the global Lipschitz-based theory is not directly releva...

Uncertain delay differential equation is a type of functional differential equations driven by canonical process. This paper presents a method to solve an uncertain delay differential equation, and proves an existence and uniqueness theorem of solution for uncertain delay differential equations under Lipschitz condition and linear growth condition by Banach fixed point theorem.

This article concerns the shunting inhibitory cellular neural networks with neutral type delays. Under a weaker condition than the usual Lipschitz condition, we establish the existence and stability of almost periodic solutions for SICNNs with neutral type delays. An example is given to illustrate our main results.

Multi-dimensional uncertain differential equation is a system of uncertain differential equations driven by amulti-dimensional Liu process. This paper first gives the analytic solutions of two special types of multi-dimensional uncertain differential equations. After that, it proves that the multi-dimensional uncertain differential equation has a unique solution provided that its coefficients s...

We characterise the weak $$^*$$ symmetric strong diameter 2 property in Lipschitz function spaces by a of its predual, Lipschitz-free space. call this new decomposable octahedrality and study duality with general. For Banach space to be decomposably octahedral it is sufficient that dual has property. Whether also necessary condition remains open.

In this paper, we study the reflected BSDE with one continuous barrier, under the monotonicity and general increasing condition on y and non Lipschitz condition on z. We prove the existence and uniqueness of the solution to these equation by approximation method.