In this work, we discuss the rate of convergence of one-dimensional random walks in a random environment. Using the hitting time decomposition, we prove that the speed of escape of random walks satisfies the quenched law of the iterated logarithm in a standard way.

The model of an immune system reaction against malignant gliomas proposed by Kronik and co-workers is simplified to the main components of the immune reaction, which are tumor cells and cytotoxic T-lymphocytes. The system has nonlinear terms with three delays, but remains tractable. For...

We discuss combined effects of stochasticity and time delays in finite-population three-player games with two mixed Nash equilibria and a pure one. We show that if basins of attraction of the stable interior equilibrium and the stable pure one are equal, then an arbitrary small time delay makes...