-
作者：Hu, Yaozhong; Jolis, Maria; Tindel, Samy
作者单位：University of Kansas; Autonomous University of Barcelona; Universite de Lorraine
摘要：In this article, we derive a Stratonovich and Skorohod-type change of variables formula for a multidimensional Gaussian process with low Holder regularity gamma (typically gamma <= 1/4). To this aim, we combine tools from rough paths theory and stochastic analysis.
-
作者：Panchenko, Dmitry
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：In many spin glass models, due to the symmetry among sites, any limiting joint distribution of spins under the annealed Gibbs measure admits the Aldous-Hoover representation encoded by a function sigma : [0, 1](4) -> {-1, +1}, and one can think of this function as a generic functional order parameter of the model. In a class of diluted models, and in the Sherrington -Kirkpatrick model, we introduce novel perturbation's of the Hamiltonian that yield certain invariance and self-consistency equat...
-
作者：Chaumont, L.
作者单位：Universite d'Angers
摘要：We show that the law of the overall supremum (X) over bar (t) = sup(s <= t) X-s of a Levy process X, before the deterministic time t is equivalent to the average occupation measure mu(+)(t) (dx) = integral(t)(0))P(X-s is an element of dx) ds, whenever 0 is regular for both open halflines (-infinity, 0) and (0, infinity). In this case, P((X) over bar (t) is an element of dx) is absolutely continuous for some (and hence for all) t > 0 if and only if the resolvent measure of X is absolutely conti...
-
作者：Asselah, Amine; Gaudilliere, Alexandre
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider a cluster growth model on Z(d), called internal diffusion limited aggregation (internal DLA). In this model, random walks start at the origin, one at a time, and stop moving when reaching a site not occupied by previous walks. It is known that the asymptotic shape of the cluster is spherical. When dimension is 2 or more, we prove that fluctuations with respect to a sphere are at most a power of the logarithm of its radius in dimension d >= 2. In so doing, we introduce a closely rel...
-
作者：Emilia Caballero, M.; Perez Garmendia, Jose Luis; Uribe Bravo, Geronimo
作者单位：Universidad Nacional Autonoma de Mexico; Instituto Tecnologico Autonomo de Mexico; Universidad Nacional Autonoma de Mexico
摘要：Guided by the relationship between the breadth-first walk of a rooted tree and its sequence of generation sizes, we are able to include immigration in the Lamperti representation of continuous-state branching processes. We provide a representation of continuous-state branching processes with immigration by solving a random ordinary differential equation driven by a pair of independent Levy processes. Stability of the solutions is studied and gives, in particular, limit theorems (of a type prev...
-
作者：Mester, Peter
作者单位：Indiana University System; Indiana University Bloomington
摘要：We show by example that there is a Cayley graph, having two invariant random subgraphs X and Y, such that there exists a monotone coupling between them in the sense that X subset of Y, although no such coupling can be invariant. Here, invariant means that the distribution is invariant under group multiplications.
