A NEW RELATION BETWEEN DIFFUSIONS AND SUPERDIFFUSIONS WITH APPLICATIONS TO THE EQUATION LU=U(ALPHA)

Authors
DYNKIN EB
Citation
Eb. Dynkin, A NEW RELATION BETWEEN DIFFUSIONS AND SUPERDIFFUSIONS WITH APPLICATIONS TO THE EQUATION LU=U(ALPHA), Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 325(4), 1997, pp. 439-444
Citations number
7
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Comptes rendus de l'Academie des sciences. Serie 1, Mathematique → ACNP
ISSN journal
07644442
Volume
325
Issue
4
Year of publication
1997
Pages
439 - 444
Database
ISI
SICI code
0764-4442(1997)325:4<439:ANRBDA>2.0.ZU;2-3
Abstract
We establish a relation between a diffusion xi and the superdiffusion X corresponding to the spatial motion xi and branching parameter alpha . It involves, on one hand, the range R and linear additive functional s of X and, on the other hand, h-transforms of process xi. By using th is relation, we investigate boundary singularities of solutions of the semilinear partial differential equation Lu = u(alpha).