In this work we study the long-time behavior for subcritical measure-valued branching processes with immigration on space of tempered measures. Under some reasonable assumptions spatial motion, and mechanisms, prove existence uniqueness an invariant measure corresponding Markov transition semigroup. Moreover, show that it converges exponential rate to unique in Wasserstein distance as well a de...

Weierstrass's everywhere continuous but nowhere diierentiable function is shown to be locally continuously fractionally diierentiable everywhere for all orders below thècritical order' 2?s and not so for orders between 2?s and 1, where s, 1 < s < 2, is the box dimension of the graph of the function. This observation is consolidated in the general result showing a direct connection between local...

Strong anomalous diffusion is characterized by asymptotic power-law growth of the moments displacement, with exponents that do not depend linearly on order moment. The concerning small-order are dominated random motion, while higher-order grow faster trajectories, such as ballistic excursions or "light fronts". Often a situation two linear dependencies their order. Here, we introduce simple exa...

Estimation methods for the Lévy density of a Lévy process are developed under mild qualitative assumptions. A classical model selection approach made up of two steps is studied. The first step consists in the selection of a good estimator, from an approximating (finite-dimensional) linear model S for the true Lévy density. The second is a data-driven selection of a linear model S, among a given...

The World Summit on Sustainable Development (Johannesburg, 2002) encouraged the application of the ecosystem approach by 2010. However, at the same Summit, the signatory States undertook to restore and exploit their stocks at maximum sustainable yield (MSY), a concept and practice without ecosystemic dimension, since MSY is computed species by species, on the basis of a monospecific model. Ackn...

In [11] an unusual connection between orthogonal polynomials and martingales has been studied. There, all orthogonal She er polynomials, were linked to a unique L evy process, i.e., a continuous time stochastic process with stationary and independent increments. The connection between the polynomials and the L evy process is expressed by a martingale relation. As an application of these marting...

In this paper, we study transition density functions for pure jump unimodal L\'evy processes killed upon leaving an open set $D$. Under some mild assumptions on the density, establish two-sided Dirichlet heat kernel estimates when $D$ is $C^{1, 1}$. Our result covers case that densities of are regularly varying whose indices equal to Euclidean dimension. This first results such weak lower scali...