68 research outputs found
A symmetry-adapted numerical scheme for SDEs
We propose a geometric numerical analysis of SDEs admitting Lie symmetries
which allows us to individuate a symmetry adapted coordinates system where the
given SDE has notable invariant properties. An approximation scheme preserving
the symmetry properties of the equation is introduced. Our algorithmic
procedure is applied to the family of general linear SDEs for which two
theoretical estimates of the numerical forward error are established.Comment: A numerical example adde
Well-posedness of a reaction-diffusion model with stochastic dynamical boundary conditions
We study the well-posedness of a nonlinear reaction diffusion partial
differential equation system on the half-line coupled with a stochastic
dynamical boundary condition, a random system arising in the description of the
evolution of the chemical reaction of sulphur dioxide with the surface of
calcium carbonate stones. The boundary condition is given by a Jacobi process,
solution to a Brownian motion-driven stochastic differential equation with a
mean reverting drift and a bounded diffusion coefficient. The main result is
the global existence and the pathwise uniqueness of mild solutions. The proof
relies on a splitting strategy, which allows to deal with the low regularity of
the dynamical boundary condition
Semi-automatic support for evolving functional dependencies
During the life of a database, systematic and frequent violations of a given constraint may suggest that the represented reality is changing and thus the constraint should evolve with it. In this paper we propose a method and a tool to (i) find the functional dependencies that are violated by the current data, and (ii) support their evolution when it is necessary to update them. The method relies on the use of confidence, as a measure that is associated with each dependency and allows us to understand \u201dhow far\u201d the dependency is from correctly describing the current data; and of goodness, as a measure of balance between the data satisfying the antecedent of the dependency and those satisfying its consequent. Our method compares favorably with literature that approaches the same problem in a different way, and performs effectively and efficiently as shown by our tests on both real and synthetic databases
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