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On the convergence of monotone schemes for path-dependent PDE

Ren, Zhenjie; Tan, Xiaolu (2017), On the convergence of monotone schemes for path-dependent PDE, Stochastic Processes and their Applications, 127, 6, p. 1738-1762. 10.1016/j.spa.2016.10.002

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Type
Article accepté pour publication ou publié
Date
2017
Journal name
Stochastic Processes and their Applications
Volume
127
Number
6
Publisher
Elsevier
Pages
1738-1762
Publication identifier
10.1016/j.spa.2016.10.002
Metadata
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Author(s)
Ren, Zhenjie
Tan, Xiaolu
Abstract (EN)
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 / Keywords
monotone schemes; Numerical analysis; viscosity solution; path-dependent PDE

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