Cónall Kelly

163 Dynamical Consistency of Solutions of Continuous and Discrete Stochastic Equations with a Finite Time Explosion John AD Appleby†, Cónall Kelly∗ and Alexandra Rodkina∗ † School of Mathematical Sciences, Dublin City ... This question is addressed in Dávila et al. ...

We identify putative load-bearing structures (bridges) in experimental colloidal systems studied by confocal microscopy. Bridges are co-operative structures that have been used to explain stability and inhomogeneous force transmission in simulated granular packings ...

ABSTRACT In the original article [LMS J. Comput. Math. 15, 71–83 (2012; Zbl 06316291)], the authors use a discrete form of the Itô formula, developed by J. A. D. Appleby et al. [Stochastics 81, No. 2, 99–127 (2009; Zbl 1177.39020)], to show that the almost sure asymptotic stability of a particular two-dimensional test system is preserved when the discretisation step size is small. In this Corrigendum, we identify an implicit assumption in the original proof of the discrete Itô formula that, left unaddressed, would preclude its application to the test system of interest. We resolve this problem by reproving the relevant part of the discrete Itô formula in such a way that confirms its applicability to our test equation. Thus, we reaffirm the main results and conclusions of the original article.

equations with coecients that take, as arguments, averaged sets of information from the history of the solution, as well as isolated past and present states. The properties that guarantee stability also guarantee positivity of solutions as long as the initial value is nonzero. We do not require that any component of the coecients of the equations satisfy Lipschitz conditions. Instead,