Unbiased local solutions of partial differential equations via the Feynman-Kac Identities Jake Carson 1 ∗ , Murray Pollock 1 and Mark Girolami 12 1 University of Warwick, Department of Statistics, UK. 2 The Alan Turing Institute for Data Science, British Library, UK. The Feynman-Kac formulae (FKF) express local solutions of par- tial differential equations (PDEs) as expectations with respect to some complementary stochastic differential equation (SDE). Repeatedly sam- pling paths from the complementary SDE enables the construction of Monte Carlo estimates of local solutions, which are more naturally suited to statistical inference than the numerical approximations ob- tained via finite difference and finite element methods. Until recently, simulating from the complementary SDE would have required the use of a discrete-time approximation, leading to biased estimates. In this paper we utilize recent developments in two areas to demonstrate that ∗ Email: Jake.Carson@warwick.ac.uk 1 arXiv:1603.04196v1 [stat.ME] 14 Mar 2016 Abstract