Recursive formulae in regularity structures

Bruned, Y., Chandra, A., Chevyrev, I., Hairer, M.: Renormalising SPDEs in regularity structures. ArXiv e-prints (2017). arXiv:1711.10239

Bruned, Y., Chevyrev, I., Friz, P.K., Preiss, R.: A rough path perspective on renormalization. ArXiv e-prints (2017). arXiv:1701.01152

Bruned, Y., Hairer, M., Zambotti, L.: Algebraic renormalisation of regularity structures. ArXiv e-prints (2016). arXiv:1610.08468

Calaque, D., Ebrahimi-Fard, K., Manchon, D.: Two interacting Hopf algebras of trees: a Hopf-algebraic approach to composition and substitution of B-series. Adv. Appl. Math 47(2), 282–308 (2011). https://doi.org/10.1016/j.aam.2009.08.003. arXiv:0806.2238

Chandra, A., Hairer, M.: An analytic BPHZ theorem for regularity structures. ArXiv e-prints (2016). arXiv:1612.08138

Chartier, P., Hairer, E., Vilmart, G.: A substitution law for B-series vector fields. Research Report RR-5498, INRIA (2005). https://hal.inria.fr/inria-00070509

Chartier, P., Hairer, E., Vilmart, G.: Algebraic structures of B-series. Found. Comput. Math. 10(4), 407–427 (2010). https://doi.org/10.1007/s10208-010-9065-1

Gubinelli, M.: Controlling rough paths. J. Funct. Anal. 216(1), 86–140 (2004). https://doi.org/10.1016/j.jfa.2004.01.002

Hairer, M.: Solving the KPZ equation. Ann. Math. (2) 178(2), 559–664 (2013). https://doi.org/10.4007/annals.2013.178.2.4. arXiv:1109.6811

Hairer, M.: A theory of regularity structures. Invent. Math 198(2), 269–504 (2014). https://doi.org/10.1007/s00222-014-0505-4. arXiv:1303.5113

Hairer, M.: The motion of a random string. ArXiv e-prints (2016). arXiv:1605.02192

Hoshino, M.: KPZ equation with fractional derivatives of white noise. Stoch. Partial Differ. Equ. Anal. Comput. 4(4), 827–890 (2016). https://doi.org/10.1007/s40072-016-0078-x. arXiv:1602.04570

Hairer, M., Pardoux, É.: A Wong–Zakai theorem for stochastic PDEs. J. Math. Soc. Jpn. 67(4), 1551–1604 (2015). https://doi.org/10.2969/jmsj/06741551. arXiv:1409.3138

Hairer, M., Quastel, J.: A class of growth models rescaling to KPZ. ArXiv e-prints (2015). arXiv:1512.07845

Hairer, M., Shen, H.: A central limit theorem for the kpz equation. Ann. Probab. 45(6B), 4167–4221 (2017). https://doi.org/10.1214/16-AOP1162

Lyons, T.: On the non-existence of path integrals. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 432(1885), 281–290 (1991). arXiv:http://rspa.royalsocietypublishing.org/content/432/1885/281.full.pdf+html. https://doi.org/10.1098/rspa.1991.0017

Shen, H., Xu, W.: Weak universality of dynamical $$\Phi ^4_3$$Φ34: non-Gaussian noise. ArXiv e-prints (2016). arXiv:1601.05724