This paper focuses on the relationships between stratified $L$-conver-gence spaces, stratified strong $L$-convergence spaces and stratifiedlevelwise  $L$-convergence spaces. It has been known that: (1) astratified $L$-convergence space is precisely a left-continuousstratified levelwise $L$-convergence space; and (2) a  stratifiedstrong $L$-convergence space is naturally a stratified $L$-converg...

This paper collects some of the well known probabilistic properties of GARCH(p, q) processes. In particular, we address the question of strictly and of weakly stationary solutions. We further investigate moment conditions as well as the strong mixing property of GARCH processes. Some distributional properties such as the tail behaviour and continuity properties of the stationary distribution ar...

We establish properties of strong local nondeterminism for several classes of α-stable random fields such as harmonizable-type fractional stable fields with stationary increments, harmonizable and linear fractional stable sheets. We apply these properties to study existence and joint continuity of the local times of stable random fields. Mathematics Subject Classification (2000). 60G52; 60G17; ...

We solve the continuity equations across an ionization front. By including a plane parallel magnetic field we find significant differences in the allowed velocities of the Rand D-type solutions between the magnetized and non-magnetized cases. These results may have implications for the study of ionization bounded diffuse sources where a moderate or strong magnetic field is expected.

Abstract: We consider a class of semilinear stochastic evolution equations driven by an additive cylindrical stable noise. We investigate structural properties of the solutions like Markov, irreducibility, stochastic continuity, Feller and strong Feller properties, and study integrability of trajectories. The obtained results can be applied to semilinear stochastic heat equations with Dirichlet...

The main purpose of this paper is to investigate constructively the relationship between proximal convergence, uniform sequential convergence and uniform convergence for sequences of mappings between apartness spaces. It is also shown that if the second space satisfies the Efremovic axiom, then proximal convergence preserves strong continuity. Mathematics Subject Classification: 54E05, 03F60

In this paper, the strong solutions (X,L) of multidimensional stochastic differential equations with reflecting boundary and possible anticipating initial random variables is established. The key is to obtain some substitution formula for Stratonovich integrals via a uniform convergence of the corresponding Riemann sums and to prove continuity of functionals of (X,L). MSC(2000): Primary 60H07, ...

In this work we investigate t-subnorms M that have strong associated negation. Firstly, we show that such t-subnorms are necessarily t-norms. Following this, we investigate the inter-relationships between different algebraic and analytic properties of such t-subnorms, viz., Archimedeanness, conditional cancellativity, left-continuity, nilpotent elements, etc. In particular, we show that under t...

in today’s turbulent world, the continuity of criticalactivities in the event of disruptions, and also fast recovery and return tobusiness as usual, are vital for sustainable success of companies. maintainingcontinuous delivery of critical business processes in the event of disruptions isa matter of business continuity. business continuity management system (bcms)is concerned with the developme...