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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.

MSC:

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

Citations:

Zbl 1357.62108
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