Volume 24, Issue 3

We investigate the effect of Ito noise on the stability of stationary solutions to a class of semilinear degenerate parabolic equations with the nonlinearity satisfying an arbitrary polynomial growth condition. We will show that an Ito noise of sufficient intensity will stabilize the unstable stationary solution.

We establish a tightness criterion in a class of Besov–Orlicz spaces. Our result generalizes those obtained in [1] in a class of standard Besov spaces and in [3] in a class of exponential Besov–Orlicz spaces. As an application, we give a limit theorem for occupation times problem of local time of a class of stochastic processes.

We consider one-dimensional stochastic equations involving local times of unknown processes. We interpret these equations as diffusion in layered media with semi-permeable barriers and we study the limit behavior of solutions as barriers compress in one barrier. Conditions for convergence in law and limit equation are obtained.

In this paper we apply the REFORM method for the deduction of the system of canonical equations K66-K69${K_{66}-K_{69}}$ for normalized spectral functions of the matrices A⁢U⁢B⁢U*${AUBU^{*}}$, where A and B are unitary nonrandom matrices and U is a random unitary matrix.

We prove, under certain conditions, the main results of the new theory (the Law of Independence for Functions of an Ensemble (LIFE)) which is based on the unusual behavior of the normalized spectral functions of the products of independent random matrices with independent normalized elements that converge at a large scale matrices with appropriate degrees of a random matrix.