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Article Dans Une Revue Stochastic Processes and their Applications Année : 2016

On the convergence of monotone schemes for path-dependent PDE *

Résumé

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.
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hal-01247002 , version 1 (20-12-2015)

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Zhenjie Ren, Xiaolu Tan. On the convergence of monotone schemes for path-dependent PDE *. Stochastic Processes and their Applications, 2016. ⟨hal-01247002⟩
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