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作者：Chaumont, L; Doney, RA
作者单位：Sorbonne Universite; University of Manchester
摘要：Any solution of the functional equation [GRAPHICS] where B is a Brownian motion, behaves like a reflected Brownian motion, except when it attains a new maximum: we call it an alpha-perturbed reflected Brownian motion. Similarly any solution of [GRAPHICS] behaves like a Brownian motion except when it attains a new maximum or minimum: we call it an alpha,beta-doubly perturbed Brownian motion. We complete some recent investigations by showing that for all permissible values of the parameters alph...
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作者：Delmas, JF
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：We consider a super-Brownian motion X. Its canonical measures can be studied through the path-valued process called the Brownian snake. We obtain the limiting behavior of the volume of the epsilon-neighborhood for the range of the Brownian snake, and as a consequence we derive the analogous result for the range of super-Brownian motion and for the support of the integrated super-Brownian excursion. Then we prove the support of X-t is capacity-equivalent to [0, 1](2) in R-d, d greater than or e...
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作者：Barral, J
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：Here, a Mandelbrot measure is a statistically self-similar measure mu on the boundary of a c-ary tree, obtained by multiplying random weights indexed by the nodes of the tree. We take a particular interest in the random variable Y = parallel to mu parallel to : we study the existence of finite moments of negative orders for Y, conditionally to Y > 0, and the continuity properties of Y with respect to the weights. Our results on moments make possible to study, with probability one, the existenc...
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作者：Wu, LM
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Clermont Auvergne (UCA)
摘要：Let L := Delta/2 + (del phi/phi) . del be a generalized Schrodinger operator or generator of Nelson's diffusion, defined on C-0(infinity)(D) where phi is a continuous and strictly positive function on an open domain D subset of R-d such that del phi is an element of L-loc(2)(D). Some results are given about the two questions below: (i) Whether does L generate a unique semigroup in L-1(D, phi(2) dx)? (ii) Whether the semigroup determined by L is strong Feller?
