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
TypeArticle accepté pour publication ou publié
Journal nameStochastic Processes and their Applications
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Abstract (EN)We propose a reformulation of the convergence theorem of monotone numerical schemes introduced by Zhang and Zhuo  for viscosity solutions of path-dependent PDEs (PPDE), which extends the seminal work of Barles and Souganidis  on the viscosity solution of PDE. We prove the convergence theorem under conditions similar to those of the classical theorem in . 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 / Keywordsmonotone schemes; Numerical analysis; viscosity solution; path-dependent PDE
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