We classify the gauge-invariant ideals in the C∗-algebras of infinite directed graphs, and describe the quotients as graph algebras. We then use these results to identify the gauge-invariant primitive ideals in terms of the structural properties of the graph, and describe the K-theory of the C∗-algebras of arbitrary infinite graphs.

The long time behavior and detailed convergence analysis of Langevin equations have received increased attention in recent years. Difficulties arise from a lack coercivity, usually termed hypocoercivity, the underlying kinetic Fokker–Planck operator, which is consequence partially deterministic nature second order stochastic differential equation. In this manuscript, effect controlling confinem...

Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for stochastic ordinary differential equations is relatively mature. In this paper, we present a unified theory of invariant manifolds for infinite dimensional random ...

In this paper, we investigate the long-time behavior of stochastic reaction– diffusion equations of the type du = (Au + f (u))dt + σ(u)dW (t), where A is an elliptic operator, f and σ are nonlinear maps and W is an infinite-dimensional nuclear Wiener process.The emphasis is onunboundeddomains.Under the assumption that the nonlinear function f possesses certain dissipative properties, this equat...