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On the convergence of monotone schemes for path-dependent PDEs
- Source :
- Stochastic Processes and their Applications. 127:1738-1762
- Publication Year :
- 2017
- Publisher :
- Elsevier BV, 2017.
-
Abstract
- We propose a reformulation of the convergence theorem of monotone numerical schemes introduced by Zhang and Zhuo [32] for viscosity solutions of path-dependent PDEs (PPDE), which extends the seminal work of Barles and Souganidis [1] on the viscosity solution of PDE. We prove the convergence theorem under conditions similar to those of the classical theorem in [1]. These conditions are satisfied, to the best of our knowledge, by all classical monotone numerical schemes in the context of stochastic control theory. In particular, the paper provides a unified approach to prove the convergence of numerical schemes for non-Markovian stochastic control problems, second order BSDEs, stochastic differential games etc.
- Subjects :
- Statistics and Probability
Stochastic control
Applied Mathematics
Numerical analysis
010102 general mathematics
Context (language use)
01 natural sciences
010104 statistics & probability
Monotone polygon
Modeling and Simulation
Viscosity (programming)
Convergence (routing)
Applied mathematics
0101 mathematics
Viscosity solution
Differential (mathematics)
Mathematics
Subjects
Details
- ISSN :
- 03044149
- Volume :
- 127
- Database :
- OpenAIRE
- Journal :
- Stochastic Processes and their Applications
- Accession number :
- edsair.doi...........77d865db1ecbec3eb2eb7df1cc88563f