We prove error bounds in a central limit theorem for solutions of certain convolution equations. The main motivation for investigating these equations stems from applications to lace expansions, in particular to weakly self-avoiding random walks in high dimensions. As an application we treat such self-avoiding walks in continuous space. The bounds obtained are sharper than those obtained by other methods.
"A local CLT for convolution equations with an application to weakly self-avoiding random walks." Ann. Probab. 44 (1) 206 - 234, January 2016. https://doi.org/10.1214/14-AOP971