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n ≥ 2, and obtain an inequality satisfied by the real and imaginary part of every eigenvalue of A (Section 3).In turn, this inequality gives rise to a region in the complex plane
Walsh’s theory of martingale measures in order to deal with stochastic partial differential equations that are second order in time, such as the wave equation and the beam equation,
Since its intrinsic metric of this Dirichlet form is just the L 2 -Wasserstein distance on P , this process is usually called Wasserstein diffusion... We shall only prove (i), and
It is thus not possible to construct the com- ponent of the vacant set containing the root of a given tree as a sequence of independent genera- tions, which is a key property
We prove that for symmetric Markov processes of diffusion type admitting a “carré du champ”, the Poincaré inequality is equivalent to the exponential convergence of the
Zhang’s model differs from the abelian sandpile model on a finite grid Λ in the following respects: The configuration space is [ 0, 1 ) Λ , rather than {0, 1,. The model evolves,
(1983) Semigroups of Linear Operators and Applications to Partial Differential Equations. (1994) Some Formulae and Estimates for the Derivative of Diffusion
Sawano and Tanka(see [13]) introduced the Morrey spaces on the non-homogeneous spaces and proved the boundedness of Hardy-Littlewood maximal operators, Calder´ on- Zygmund operators
