Exponential stability for stochastic differential equation driven by G-Brownian motion

AbstractConsider a stochastic differential equation driven by G-Brownian motion dX(t)=AX(t)dt+σ(t,X(t))dBt which might be regarded as a stochastic perturbed system of dX(t)=AX(t)dt. Suppose the second equation is quasi surely exponentially stable. In this paper, we investigate the sufficient conditions under which the first equation is still quasi surely exponentially stable

A Strong Law of Large Numbers for Weighted Sums of i.i.d. Random Variables under Capacities

With the notion of independent identically distributed (i.i.d.) random variables under sublinear expectations initiated by Peng, a strong law of large numbers for weighted sums of i.i.d. random variables under capacities induced by sublinear expectations is obtained

The EHTA for Two Shallow Water Wave Equations

Abstract In this paper, two shallow water wave equations are studied by using the extended homoclinic test approach (EHTA). The new exact solutions for the shallow water wave equations are obtained. Their dynamic properties of some exact solutions are discussed and their profiles of these solutions are given by using of software Maple. Mathematics Subject Classification: 35B05, 35B10, 35B1