Invariant measures for hybrid stochastic systems

Invariant Clusters for Hybrid Systems

In this paper, we propose an approach to automatically compute invariant clusters for semialgebraic hybrid systems. An invariant cluster for an ordinary differential equation (ODE) is a multivariate polynomial invariant g(~u, ~x) = 0, parametric in ~u, which can yield an infinite number of concrete invariants by assigning different values to ~u so that every trajectory of the system can be over...

Invariant manifold reduction for stochastic dynamical systems

Invariant manifolds facilitate the understanding of nonlinear stochastic dynamics. When an invariant manifold is represented approximately by a graph for example, the whole stochastic dynamical system may be reduced or restricted to this manifold. This reduced system may provide valuable dynamical information for the original system. The authors have derived an invariant manifold reduction or r...

Concentration of Invariant Measures for Stochastic Generalized Porous Media Equations

By using Bernstein functions, existence and concentration properties are studied for invariant measures of the infinitesimal generators associated to a large class of stochastic generalized porous media equations. In particular, results derived in [4] are extended to equations with non-constant and stronger noises. Analogous results are also proved for invariant probability measures for strong ...

Invariant measures for Burgers equation with stochastic forcing

Gibbsian Dynamics and Invariant Measures for Stochastic Dissipative PDEs

1 Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544; and School of Mathematical Sciences, Peking University, People’s Republic of China; e-mail: [email protected] 2 Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544; e-mail: [email protected] Received June 30, 200...