Fully nonlinear stochastic pde with semilinear stochastic dependence

Authors
Lions, PL Souganidis, PE
Citation
Pl. Lions et Pe. Souganidis, Fully nonlinear stochastic pde with semilinear stochastic dependence, CR AC S I, 331(8), 2000, pp. 617-624
Citations number
19
Categorie Soggetti
Mathematics
Journal title
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE
ISSN journal
07644442 → ACNP
Volume
331
Issue
8
Year of publication
2000
Pages
617 - 624
Database
ISI
SICI code
0764-4442(20001015)331:8<617:FNSPWS>2.0.ZU;2-P
Abstract
We study in this Note scalar fully nonlinear stochastic second order partia l differential equations, possibly, degenerate with a semilinear stochastic dependence. We introduce a notion of stochastic viscosity solutions adapte d to that class of equations. And we show general existence, uniqueness and regularity results. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.