2001/05/28 by Igor Chueshov, Igor Čhuešhov, Chueshov, Igor +5
Computer Science · Economics, Econometrics and Finance · Engineering · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #nlin.CD #nlin.PS
paper · pdf · doi:10.48550/arxiv.nlin/0105062
To appear: Nonlinear Diff Eqns and Applications (NoDEA)
arxiv created 2001/05/28 · arxiv updated 2009/11/30
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional \em random dynamical systems. In these applications the convergence condition of the trajectories of an infinite dimensional random dynamical system with respect to a finite set of linear functionals is assumed to be either in mean or exponential with respect to the convergence almost surely. In contrast to these ideas we introduce a convergence concept which is based on the convergence in probability. By this ansatz we get rid of the assumption of exponential convergence. In addition, setting the random terms to zero we obtain usual deterministic results. We apply our results to the 2D Navier - Stokes equations forced by a white noise.