On the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion with integral-Lipschitz coefficients

Abstract

Abstract. In this paper, we study the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion (GSDEs) with integral-Lipschitz conditions on their coefficients.

Formation of multi-armed spiral waves in neuronal network induced by adjusting ion channel conductance

“…The results are consistent with those from previous studies 38 and the stability of multi-armed spirals can be further discussed as shown in Ref. 42. These findings explain why multi-spiral waves seldom emerge and are not as common as spiral waves with a single arm.…”

“…Zaritski et al 41 numerically investigated the parameter region for generating multi-armed spiral wave with different arm numbers. Bai et al 42 gave numerical analysis about the multi-armed spiral waves in gas discharge system. As reported by Ref.…”

Quadratic backward stochastic differential equations driven by G-Brownian motion: Discrete solutions and approximation

“…To verify that {Ȳ n } n∈N is a Cauchy sequence in S Indeed, since w h is a concave function, by Lemma 2.12 in Bai and Lin [2], we have…”

The cocycle property of stochastic differential equations driven by G-Brownian motion

“…The unique solution to (1.1) is constructed through successive approximation. It is worthwhile to mention that non-Lipschitz conditions have been studied in [2]. But our assumption is more general than theirs.…”