Existence and uniqueness of solutions to the stochastic heat equation with multiplicative
spatial noise is studied. In the spirit of pathwise regularization by noise, we show that a …

We establish a multiparameter extension of the stochastic sewing lemma. This allows us to
derive novel regularity estimates on the local time of locally non-deterministic Gaussian …

This thesis concerns the study of regularisation by noise phenomena for ODEs and PDEs. In
particular, it focuses on the use of so called pathwise techniques: our aim is to identify …

Based on the notion of paracontrolled distributions, we provide existence and uniqueness
results for rough Volterra equations of convolution type with potentially singular kernels and …

Given a continuous Gaussian process x which gives rise to a p-geometric rough path for
p∈(2, 3), and a general continuous process y controlled by x, under proper conditions we …

We extend the recently developed rough path theory for Volterra equations from [F. Harang
and S. Tindel, Volterra equations driven by rough signals, Stoch. Process. Appl. 142 (2021) …

We investigate the probabilistic and analytic properties of Volterra processes constructed as
pathwise integrals of deterministic kernels with respect to the Hölder continuous trajectories …

Over the past decade, the importance of the 1D signature which can be seen as a functional
defined along a path, has been pivotal in both path-wise stochastic calculus and the …

We extend the new approach introduced in [24] and [25] for dealing with stochastic Volterra
equations using the ideas of Rough Path theory and prove global existence and uniqueness …

After a brief survey on rough paths theory, from the seminal paper of T. Lyons to its recent
developments, this proceeding provides details on C. Bellingeri, Y. Bruned and A …