### $\left(2m\right)$-th mean behavior of solutions of stochastic differential equations under parametric perturbations.

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It is shown that the restricted maximal operator of the two-dimensional dyadic derivative of the dyadic integral is bounded from the two-dimensional dyadic Hardy-Lorentz space ${H}_{p,q}$ to ${L}_{p,q}$ (2/3 < p < ∞, 0 < q ≤ ∞) and is of weak type $({L}_{1},{L}_{1})$. As a consequence we show that the dyadic integral of a ∞ function $f\in {L}_{1}$ is dyadically differentiable and its derivative is f a.e.

In the paper, binary 1-Lipschitz aggregation operators and specially quasi-copulas are studied. The characterization of 1-Lipschitz aggregation operators as solutions to a functional equation similar to the Frank functional equation is recalled, and moreover, the importance of quasi-copulas and dual quasi-copulas for describing the structure of 1-Lipschitz aggregation operators with neutral element or annihilator is shown. Also a characterization of quasi-copulas as solutions to a certain functional...

We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals “on-the-fly” as well as their limiting occupation measures with a given precision degree that does not depend on the final time horizon. We...

We obtain the asymptotics for the speed of a particular case of a particle system with branching and selection introduced by Bérard and Gouéré [Comm. Math. Phys.298 (2010) 323–342]. The proof is based on a connection with a supercritical Galton–Watson process censored at a certain level.