*Correspondence: [email protected] School of Mathematics and Statistics, Chong Qing University, Chong Qing, P.R. China Abstract The existence and uniqueness of a mild solution to stochastic equations with jumps are established, a stochastic Fubini theorem and a type of Burkholder-Davis-Gundy inequality are proved, and the two formulas are used to study the regularity property of the mild sol...

This paper studies the asymptotic behavior for a class of delayed reaction-diffusion Hopfield neural networks driven by finite-dimensional Wiener processes. Some new sufficient conditions are established to guarantee the mean square exponential stability of this system by using Poincaré’s inequality and stochastic analysis technique. The proof of the almost surely exponential stability for this...

We prove that non-commutative martingale transforms are of weak type (1, 1). More precisely, there is an absolute constant C such that if M is a semi-finite von Neumann algebra and (Mn)n=1 is an increasing filtration of von Neumann subalgebras of M then for any non-commutative martingale x = (xn) ∞ n=1 in L 1(M), adapted to (Mn)n=1, and any sequence of signs (εn) ∞ n=1, ∥∥∥∥ε1x1 + N ∑ n=2 εn(xn...

Abstract We consider decoupling inequalities for random variables taking values in a Banach space X . restrict the class of distributions that appear as conditional while and show each adapted process can be approximated by Haar-type expansion which only pre-specified appear. Moreover, we our framework progressive enlargement underlying filtration does not affect properties (in particular, it c...

Introduction: Inspired by quantum mechanics and probability, non-commutative probability has become an independent field of mathematical research. We refer to P.A. Meyer’s exposition [Me], the successive conferences on quantum probability [AvW], the lecture notes by Jajte [Ja1, Ja2] on almost sure and uniform convergence and finally the work of Voiculescu, Dykema, Nica [VDN] and of Biane, Speic...

Hemicriconemoides scottolamassesei n. sp., named after Dr. C. Scotto la Massese, from New Caledonia, is described and illustrated. Primary diagnostic characters are females with a continuous head and three lip annules, the first annule being the smallest, stylet length of 65-75 mum, vulva without lateral flaps, and acute tail terminus; J4 has a smooth cuticle without scales or spines; the male ...

A common feature of plant-parasitic nematodes on annual crops is that they have an uneven distribution within a field and the symptoms of damage, normally associated with high population densities, occur in patches (McSorley,1998). Where a susceptible annual crop is replanted year after year the nematodes spread and the patches increase in size and eventually coalesce (Brown, 1987; Swarup and S...