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On the existence of paths between points in high level excursion sets of Gaussian random fields
Gaussian process excursion set large deviations exceedence probabilities connected component optimal path
2012/4/17
The structure of Gaussian random fields over high levels is a well researched and well understood area, particularly if the field is smooth. However, the question as to whether or not two or more poin...
On the existence of a time inhomogeneous skew Brownian motion and some related laws
time inhomogeneous skew Brownian motion Probability
2011/9/2
Abstract: This article is devoted to the construction of a solution for the "skew inhomogeneous Brownian motion" equation, which first appear in a seminal paper by Sophie Weinryb (1983). We investigat...
Existence of random gradient states
random interfaces gradient Gibbs measures disordered systems Green function
2011/2/24
We consider two versions of random gradient models. In model A) the interface feels a bulk
term of random fields while in model B) the disorder enters though the potential acting on the
gradients it...
Martingale problems on Banach spaces -- Existence, uniqueness and the Markov property
Martingale solution strong Markov property stochastic partial differential equation
2010/12/6
We study (local) martingale problems on a general separable Banach space E and apply our results to stochastic evolution equations. In particular,we prove that if such an equation is well-posed, then ...
Existence of Linear-Quadratic Regulator for Degenerate Diffusions
Stochastic differential equation Hamilton-Jacobi-Bellman equation Linear-Quadratic problem Viscosity solutions Applications to control theory
2010/2/26
This paper studies a linear regulatory quadratic control problem for degenerate Hamilton-Jacobi-Bellman (HJB) equation. We establish the existence of a unique viscosity and a classical solution of the...