zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Generalized reflected BSDEs driven by a Lévy process and an obstacle problem for PDIEs with a nonlinear Neumann boundary condition. (English) Zbl 1217.60047
The authors study a class of generalized reflected backward stochastic differential equations (GRBSDEs) driven by the Teugels martingales associated with a Lévy process as well as by a square integrable increasing process; the reflecting lower barrier is supposed to be square integrable and càdlàg. The present work generalizes earlier results of E. Pardoux and S. Zhang [Probab. Theory Relat. Fields 110, No. 4, 535–558 (1998; Zbl 0909.60046)], M. El Otmani [J. Appl. Math. Stochastic Anal. 2006, Article ID 85407 (2006; Zbl 1147.60319)] and N. El Karoui, C. Kapoudjian, E. Pardoux, S. Peng and M. C. Quenez [Ann. Probab. 25, No. 2, 702–737 (1997; Zbl 0899.60047)] by bringing together the concepts of generalized backward stochastic differential equations and reflected backward stochastic differential equations. Let us also mention that Y. Ren and L. Hu [Stat. Probab. Lett. 77, No. 15, 1559–1566 (2007; Zbl 1128.60048)] studied reflected backward stochastic differential equations driven by Teugels martingales and an independent Brownian motion. By combining the methods developed in these four papers, the authors of the present work prove the existence and the uniqueness of the solution. For this, they use the Snell envelope, the penalization method and a fixed point theorem. Furthermore, they prove a comparison theorem for the solutions of GRBSDEs. In the end, they give in terms of a forward equation and an associated GRBSDE the probabilistic interpretation for the viscosity solution of an obstacle problem for partial differential-integral equations with a nonlinear Neumann boundary condition.
MSC:
60H10Stochastic ordinary differential equations
60G51Processes with independent increments; Lévy processes
35K60Nonlinear initial value problems for linear parabolic equations