Lower estimates of transition densities and bounds on exponential ergodicity for stochastic PDEs

Goldys, B.; Maslowski, B.

Ann. Probab., Tome 34 (2006) no. 1, p. 1451-1496 / Harvested from Project Euclid

Résumé

A formula for the transition density of a Markov process defined by an infinite-dimensional stochastic equation is given in terms of the Ornstein–Uhlenbeck bridge and a useful lower estimate on the density is provided. As a consequence, uniform exponential ergodicity and V-ergodicity are proved for a large class of equations. We also provide computable bounds on the convergence rates and the spectral gap for the Markov semigroups defined by the equations. The bounds turn out to be uniform with respect to a large family of nonlinear drift coefficients. Examples of finite-dimensional stochastic equations and semilinear parabolic equations are given.

Publié le : 2006-07-14
Classification: Ornstein–Uhlenbeck bridge, stochastic semilinear system, density estimates, V-ergodicity, uniform exponential ergodicity, spectral gap, 35R60, 37A30, 47A35, 60H15, 60J99

@article{1158673324,
     author = {Goldys, B. and Maslowski, B.},
     title = {Lower estimates of transition densities and bounds on exponential ergodicity for stochastic PDEs},
     journal = {Ann. Probab.},
     volume = {34},
     number = {1},
     year = {2006},
     pages = { 1451-1496},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1158673324}
}

Goldys, B.; Maslowski, B. Lower estimates of transition densities and bounds on exponential ergodicity for stochastic PDEs. Ann. Probab., Tome 34 (2006) no. 1, pp.  1451-1496. http://gdmltest.u-ga.fr/item/1158673324/