Self-Intersection Local Time of (α,d,β)(\alpha,d,\beta)-superprocess

The existence of self-intersection local time (SILT), when the time diagonal is intersected, of the $(\alpha,d,\beta)$-superprocess is proved for $d/2<\alpha$ and for a renormalized SILT when $d/(2+(1+\beta)^{-1})<\alpha \leq d/2$. We also establish Tanaka-like formula for SILT.Comment: 28 page

Regularity of Ornstein-Uhlenbeck processes driven by a L{\'e}vy white noise

The paper is concerned with spatial and time regularity of solutions to linear stochastic evolution equation perturbed by L\'evy white noise "obtained by subordination of a Gaussian white noise". Sufficient conditions for spatial continuity are derived. It is also shown that solutions do not have in general \cadlag modifications. General results are applied to equations with fractional Laplacian. Applications to Burgers stochastic equations are considered as well.Comment: This is an updated version of the same paper. In fact, it has already been publishe

Mutually catalytic branching in the plane: Infinite measure states

A two-type infinite-measure-valued population in R2 is constructed which undergoes diffusion and branching. The system is interactive in that the branching rate of each type is proportional to the local density of the other type. For a collision rate sufficiently small compared with the diffusion rate, the model is constructed as a pair of infinite-measure-valued processes which satisfy a martingale problem involving the collision local time of the solutions. The processes are shown to have densities at fixed times which live on disjoint sets and explode as they approach the interface of the two populations. In the long-term limit (in law), local extinction of one type is shown. Moreover the surviving population is uniform with random intensity. The process constructed is a rescaled limit of the corresponding Z 2-lattice model studied by Dawson and Perkins (1998) and resolves the large scale mass-time-space behavior of that model under critical scaling. This part of a trilogy extends results from the finite-measure-valued case, whereas uniqueness questions are again deferred to the third part

Stochastic Reaction-diffusion Equations Driven by Jump Processes

We establish the existence of weak martingale solutions to a class of second order parabolic stochastic partial differential equations. The equations are driven by multiplicative jump type noise, with a non-Lipschitz multiplicative functional. The drift in the equations contains a dissipative nonlinearity of polynomial growth.Comment: See journal reference for teh final published versio

Eight new species of Gomphichis (Orchidaceae, Spiranthoideae) from Colombia

Eight new species of the genus Gomphichis from Colombia are described. Each species is illustrated, and detailed habitat and distribution data are provided. A distribution map of the new species is presented. A dichotomous key for determination of the Gomphichis species in northern South America is provided. Conservation status assessments are provided for each species; current International Union for Conservation of Nature (IUCN) Red List categories and criteria are listed. A brief discussion of spiranthoid orchids taxonomy, conservation status of species, endemism in the Andes and paramo are presented

Novelties in African Orchidaceae: new taxa from Central-West Africa

Volume: 10Start Page: 125End Page: 14

Scolopendrogyne and Scolopendrogyninae, new genus and new subtribe in the tribe Oncidieae (Vandoideae, Orchidaceae)

Volume: 9Start Page: 204End Page: 20