Stochastic partial differential equations for a class of interacting measure-valued diffusions
Stochastic processes on random domains
Stochastic representation of reflecting diffusions corresponding to divergence form operators
We obtain a stochastic representation of a diffusion corresponding to a uniformly elliptic divergence form operator with co-normal reflection at the boundary of a bounded -domain. We also show that the diffusion is a Dirichlet process for each starting point inside the domain.
Stochastic stability of neural networks with both Markovian jump parameters and continuously distributed delays.
Stochastic vortices in periodically reclassified populations
Our paper considers open populations with arrivals and departures whose elements are subject to periodic reclassifications. These populations will be divided into a finite number of sub-populations. Assuming that: a) entries, reclassifications and departures occur at the beginning of the time units; b) elements are reallocated at equally spaced times; c) numbers of new elements entering at the beginning of the time units are realizations...
Stokes efficiency of molecular motor-cargo systems.
Stopping Markov processes and first path on graphs
Given a strongly stationary Markov chain (discrete or continuous) and a finite set of stopping rules, we show a noncombinatorial method to compute the law of stopping. Several examples are presented. The problem of embedding a graph into a larger but minimal graph under some constraints is studied. Given a connected graph, we show a noncombinatorial manner to compute the law of a first given path among a set of stopping paths.We prove the existence of a minimal Markov chain without oversized information....
Stopping sequences
Strangely sweeping one-dimensional diffusion
Let X(t) be a diffusion process satisfying the stochastic differential equation dX(t) = a(X(t))dW(t) + b(X(t))dt. We analyse the asymptotic behaviour of p(t) = ProbX(t) ≥ 0 as t → ∞ and construct an equation such that and .
Strassen theorem in holder norm for some brownian functionals
Stratonovich stochastic differential equations driven by general semimartingales
Strict concavity of the half plane intersection exponent for planar Brownian motion.
Strict concavity of the intersection exponent for Brownian motion in two and three dimensions.
Strict fine maxima.
Strict Potentials and Hunt Processes.
Strong and weak stability of some Markov operators
An integral Markov operator appearing in biomathematics is investigated. This operator acts on the space of probabilistic Borel measures. Let and be probabilistic Borel measures. Sufficient conditions for weak and strong convergence of the sequence to are given.
Strong existence, uniqueness and non-uniqueness in an equation involving local time
Strong Feller solutions to SPDE's are strong Feller in the weak topology
For a wide class of Markov processes on a Hilbert space H, defined by semilinear stochastic partial differential equations, we show that their transition semigroups map bounded Borel functions to functions weakly continuous on bounded sets, provided they map bounded Borel functions into functions continuous in the norm topology. In particular, an Ornstein-Uhlenbeck process in H is strong Feller in the norm topology if and only if it is strong Feller in the bounded weak topology. As a consequence,...
Strong law of large numbers for branching diffusions
Let X be the branching particle diffusion corresponding to the operator Lu+β(u2−u) on D⊆ℝd (where β≥0 and β≢0). Let λc denote the generalized principal eigenvalue for the operator L+β on D and assume that it is finite. When λc>0 and L+β−λc satisfies certain spectral theoretical conditions, we prove that the random measure exp{−λct}Xt converges almost surely in the vague topology as t tends to infinity. This result is motivated by a cluster of articles due to Asmussen and Hering dating from...
Strong law of large numbers for fragmentation processes
In the spirit of a classical result for Crump–Mode–Jagers processes, we prove a strong law of large numbers for fragmentation processes. Specifically, for self-similar fragmentation processes, including homogenous processes, we prove the almost sure convergence of an empirical measure associated with the stopping line corresponding to first fragments of size strictly smaller than η for 1≥η>0.