Lyapunov Exponent and Rotation Number of Two-Dimensional Linear Stochastic Systems with Small Diffusion

Pathwise Stability of Degenerate Stochastic Evolutions

“…IEOT For more results on finite dimensional stochastic Lyapunov exponents, see the overview paper [4], the book by Khasminskii [22], and e.g. [2,3,24,31] and [33].…”

Random attractions and bifurcation for the classical Rayleigh–van der Pol equations with small noise

“…For small σ 1 , σ 2 we can use the asymptotic expansion given by Pardoux and Wihstutz [26] and others, namely when σ 1 → 0, σ 2 → 0, then Lyapunov exponent of (3.4)…”

Stabilization of evolution equations by noise

“…The problem of stabilization of ordinary differential equations by noise, in terms of almost sure Lyapunov exponents, has been thoroughly studied (see for instance [2], [3], [4], [9] and [10]). However, for the time being, to our knowledge, there are very few results concerning stochastic stabilization in the infinite-dimensional case.…”