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Shao (2009), the inequality (1.2) has been applied to prove the necessary upper and lower bounds in Theorem 8.6 in order to obtain the moderate deviation result for
We prove an almost sure limit theorem on the exact convergence rate of the maximum of standardized gaussian random walk increments.. On a conjecture of R´
It is known from the multiplicative ergodic theorem that the norm of the derivative of certain stochastic flows at a previously fixed point grows exponentially fast in time as the
We are now in position to state our main result in this article (Theorem 1.2.1). It extends our previous result [NY09a, Theorem 1.2.1] to wider class of models so that it covers
Theorem 1.3 establishes the relationships among the dual Hardy inequality (1.7), the first Dirichlet eigenvalue λ 0 and the first eigenvalue λ 0,T of transient diffusion
The proof of Theorem 3 is based on Burkholder’s technique, which reduces the problem of proving a martingale inequality to finding a certain spe- cial function.. The description of
The main step in the proof of Theorem 1 (ii) will be Theorem 10 below, which states that within a cube of appropriate size, the final configuration of the model resembles
Our paper will be a first step in a complete Minkowski space Hamiltonian treatment of Liouville field theory on a strip with independent FZZT type boundary conditions on both
