The energy functional, balayage, and capacity
The energy representation of Sobolev-Lie groups
The entrance boundary of the multiplicative coalescent.
The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice
The ergodic theory of positive operators on continuous functions
The escape model on a homogeneous tree.
The evolution and Poisson kernels on nilpotent meta-abelian groups
Let S be a semidirect product S = N⋊ A where N is a connected and simply connected, non-abelian, nilpotent meta-abelian Lie group and A is isomorphic to , k>1. We consider a class of second order left-invariant differential operators on S of the form , where , and for each is left-invariant second order differential operator on N and , where Δ is the usual Laplacian on . Using some probabilistic techniques (e.g., skew-product formulas for diffusions on S and N respectively) we obtain an...
The exact asymptotic of the time to collision.
The excessive domination principle is equivalent to the weak sector condition
The existence and exponential stability for random impulsive integrodifferential equations of neutral type.
The existence of a multiple spider martingale in the natural filtration of a certain diffusion in the plane
The Existence of Dual Processes.
The Existence of Measurable Approximating Maximums.
The existence of the potential operator associated with an equicontinuous semigroup of class
The exit path of a Markov chain with rare transitions
The exit path of a Markov chain with rare transitions
We study the exit path from a general domain after the last visit to a set of a Markov chain with rare transitions. We prove several large deviation principles for the law of the succession of the cycles visited by the process (the cycle path), the succession of the saddle points gone through to jump from cycle to cycle on the cycle path (the saddle path) and the succession of all the points gone through (the exit path). We estimate the time the process spends in each cycle of the cycle path...
The exit place of Brownian motion in an unbounded domain.
The exit place of Brownian motion in the complement of a horn.
The expected cumulative operational time for finite semi-Markov systems and estimation
In this paper we, firstly, present a recursive formula of the empirical estimator of the semi-Markov kernel. Then a non-parametric estimator of the expected cumulative operational time for semi-Markov systems is proposed. The asymptotic properties of this estimator, as the uniform strongly consistency and normality are given. As an illustration example, we give a numerical application.
The expected discounted reward from a Markov replacement process