This paper is concerned with the problem of explosive solutions for a class of stochastic differential equations. Our main results are presented as two theorems. Theorem 1 is concerned with the existence of explosive solutions with positive probability under certain sufficient conditions. With...

We compute the second order correction for the cover time of the binary tree of depth n by (continuous-time) random walk, and show that with probability approaching 1 as n increases, τcov=|E|[2log2⋅n−logn/2log2+O((loglogn)8)], thus showing that the second order correction differs from the...

The problem of exit from a domain of attraction of a stable equilibrium point in the presence of small noise is considered for a class of two-dimensional systems. It is shown that for these systems, the exit measure is 'skewed' in the sense that if S denotes the saddle point in the...

Recursive parameter estimation in diffusion processes is considered. First, stability and asymptotic properties of the global, off-line MLE (maximum likelihood estimator) are obtained under explicit conditions. The MLE evolution equation is then derived by employing a generalized Itô...

We analyse the quasi-stationary distributions of the family of Markov chains {Xn[var epsilon]},[var epsilon]0, obtained from small non-local random perturbations of iterates of a map f : I--I on a compact interval. The class of maps considered is slightly more general than the class of...

We investigate, by means of an example, the large deviations principle for the empirical measure of a Markov chain when Feller continuity properties are not assumed. Using the weak convergence approach, we explicitly compute the resulting rate function, and find that it is not of the...