Comment on article by Chkrebtii, Campbell, Calderhead and Girolami. (English) Zbl 1357.62119

Summary: O. A. Chkrebtii et al. [ibid. 11, No. 4, 1239–1267 (2016; Zbl 1357.62108)] present an ingenious probabilistic numerical solver for deterministic differential equations (DEs). The true solution is progressively identified via model interrogations, in a formal framework of Bayesian updating. I have attempted to extend the authors’ ideas to stochastic differential equations (SDEs), and discuss two challenges encountered in this endeavor: (i) the non-differentiability of SDE sample paths, and (ii) the sampling of diffusion bridges, typically required of solutions to the SDE inverse problem.


62F15 Bayesian inference
65C60 Computational problems in statistics (MSC2010)
65C05 Monte Carlo methods
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
35R99 Miscellaneous topics in partial differential equations


Zbl 1357.62108