## Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order.(English)Zbl 0893.60036

Decreusefond, Laurent (ed.) et al., Stochastic analysis and related topics VI. Proceedings of the 6th Oslo-Silivri workshop, Geilo, Norway, July 29–August 6, 1996. Boston, MA: Birkhäuser. Prog. Probab. 42, 79-127 (1998).
Linear backward stochastic differential equations, in short BSDEs, appeared already a long time ago in stochastic control, but only in 1990, with the first paper on nonlinear BSDEs by E. Pardoux and S. G. Peng [Syst. Control Lett. 14, No. 1, 55-61 (1990; Zbl 0692.93064)], and the paper by S. Peng in 1991 about the interpretation of BSDE as generalization of the Feynman-Kac formula to systems of quasilinear parabolic PDEs, a very dynamic development of the subject has started and a lot of authors have worked on. This great interest is to explain by the vaste possibilities of application of BSDEs in stochastic control, in finance, in construction of $$\Gamma$$-martingales and, last not least, in PDE problems. The author of the present work who himself has made a lot of important contributions in this subject, develops the actual theory (including proofs) of BSDEs and its connection with PDE, in particular, in the context of viscosity solution. This excellent review is completed by a long list of references and should allow the reader knowing stochastic analysis to familiarize with BDEs and actual developments in this theory.
For the entire collection see [Zbl 0880.00043].
Reviewer: R.Buckdahn (Brest)

### MSC:

 60H15 Stochastic partial differential equations (aspects of stochastic analysis)

Zbl 0692.93064