Abstract The central limit theorem for the resolvent of random Gram matrices with stochastically independent column vectors is proven. Due to its importance in MAGIC (Mathematical Analysis of Global Invisible Components), this result is called the Brilliant Law.
Abstract In this paper, we establish several new deterministic and random fixed point theorems for applications satisfying some condition via concept of degree of nondensifiability (DND for short). The results hire extend some classical new and results in the literature. Furthermore, we apply main results, for study the existence of random solution for some classes of fractional differential equations with Cauchy condition.
In this paper, under non-Lipschitz condition, we shall prove the homeomorphic flow property of solution to multidimensional stochastic differential equation (SDE) driven simultaneously by fractional Brownian motion with H is an element of ( 1 2 , 1 ) {H\in(\frac{1}{2},1)} and standard Brownian motion.
In this paper, we establish the existence and uniqueness of a solution for multidimensional generalized backward stochastic differential equations where the noise is driven by a Brownian motion and an independent Poisson random measure. We consider the case where the generators are weakly monotone and satisfy a general growth condition. Our results are derived using a priori estimates, the convolution approach and truncation techniques
Employing an iterative method, we establish the existence and uniqueness solution of psi-Riemann-Liouville fractional stochastic differential equations. Examples are provided to illustrate our results.
