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Geometric Influences II: Correlation Inequalities and Noise Sensitivity
Influences geometric influences noise sensitivity correlation between increasing sets Talagrand’s bound Gaussian measure isoperimetric inequality
2012/6/25
In a recent paper, we presented a new definition of influences in product spaces of continuous distributions, and showed that analogues of the most fundamental results on discrete influences, such as ...
Multiplicative white noise functionals and the Krylov-Veretennikov expansion for coalescing stochastic flows
Krylov-Veretennikov expansion coalescing stochastic flows Probability
2011/9/20
Abstract: In this article we consider multiplicative operator-valued white noise functionals related to a stochastic flow. A generalization of the Krylov-Veretennikov expansion is presented. An analog...
Noise as a Boolean algebra of sigma-fields. I. Completion
Noise Boolean algebra of sigma-fields Probability
2011/9/9
Abstract: Nonclassical noises over the plane (such as the black noise of percolation) consist of sigma-fields corresponding to some planar domains. One can treat less regular domains as limits of more...
Small Noise Asymptotics for Invariant Densities for a Class of Diffusions: A Control Theoretic View (with Erratum)
diffusions invariant density small noise limit Hamilton-Jacobi equation viscosity solution
2011/9/2
Abstract: The uniqueness argument in the proof of Theorem 5, p. 483, of "Small noise asymptotics for invariant densities for a class of diffusions: a control theoretic view, J. Math. Anal. and Appl. (...
Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications
Harnack inequality functional solution delay SDE strong Feller property
2011/2/28
By constructing a new coupling, the log-Harnack inequality is established for the functional solution of a delay stochastic differential equation with multiplicative noise. As applications, the strong...
Low noise limit for the invariant measure of a multi-dimensional stochastic Allen-Cahn equation
Stochastic reaction-di usion equation Invariant measure Large deviations
2011/1/21
We study the invariant measure of a discretized stochastic Allen-Cahn equation in d+1 dimensions in the low noise limit. We consider a cuboidal domain and impose the two stable
phases as boundary con...
Hydrodynamic Limit for an Hamiltonian System with Boundary Conditions and Conservative Noise
Intuitionistic fuzzy differentiation intuitionistic fuzzy continuity
2010/12/3
ntuitionistic Fuzzy derivative, Intuitionistic Fuzzy Gateaux derivative, Intuitionistic Fuzzy Fr´echet derivative are defined and a few of their properties are studied. The relation be-
tween I...
Filtering of continuous-time Markov chains with noise-free observation and applications
Filtering of continuous-time Markov chains noise-free observation applications
2010/11/30
Let X be a continuous-time Markov chain in a finite set I, let h be a mapping of I onto another set, and let Y be defined by Yt = h(Xt), (t ≥ 0). We address the filtering problem
for X in terms of th...