Fractal dimensions of random attractors for stochastic Benjamin-Bona-Mahony equation on unbounded domains

This paper considers random attractor and its fractal dimension for Benjamin-Bona-Mahony equation driven by additive white noise on unbounded domains . Firstly, we investigate the existence of random attractor for the random dynamical system defined on an unbounded domain. Secondly, we present criterion for estimating an upper bound of the fractal dimension of a random invariant set of a random dynamical system on a separable Banach space. Finally, we apply expectations of some random variables and these conditions to prove the finiteness of fractal dimension of the random attractors for stochastic Benjamin-Bona-Mahony equation driven by additive white noise.