Space weather events such as solar flares can be harmful for life and infrastructure on Earth or in near‐Earth orbit. In this paper we employ extreme value theory to model extreme solar flare events; extreme value theory offers the appropriate tools for the study and estimation of probabilities for extrapolation to ranges outside of those that have already been observed. In this work the data points used are inherently independent and realistic confidence intervals are offered with respect to the estimates of future solar flare events. The data used in this study are peak X‐ray fluxes provided by National Oceanic and Atmospheric Administration that form a series of distinct flare events. The expected return levels for Carrington‐ or Halloween storm‐like events were calculated with the outcome that the existing data predict similar events happening in 110 and 38 years, respectively, which are consistent with the results and inferences provided by Elvidge and Angling (2018, https://doi.org/10.1002/2017SW001727). We also make a preliminary analysis of the implications of solar seasonality and found its effect on extreme flare events to be statistically insignificant.

In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this "worldline Monte Carlo" approach to the standard problem of the numerical approximation of the non-relativistic path integral, resulting in a formalism whose characteristic feature is the fast, non-recursive generation of an ensemble of trajectories that is independent of the potential, and thus universally applicable. The numerical implementation discretises the trajectories with respect to their time parametrisation but maintains a continuous spatial domain. In the case of singular potentials, the discretised action gets adapted to the singularity through a "smoothing" procedure. We show for a variety of examples (the harmonic oscillator in various dimensions, the modified Pöschl-Teller potential, delta-function potentials, the Coulomb and Yukawa potentials) that the method allows one to obtain fast and reliable estimates for the Euclidean propagator and use them in a certain time window suitable for extracting the ground state energy. As an aside, we apply it for studying the classical limit where nearly classical trajectories are expected to dominate in the path Email addresses: jedwards@ifm.umich.mx (James P. Edwards), gerberu@itp.unibe.ch (Urs Gerber), schubert@ifm.umich.mx (Christian Schubert), mtrejo@ifm.umich.mx (Maria Anabel Trejo), ttsiftsi@matmor.unam.mx (Thomai Tsiftsi), axel@ifm.umich.mx (Axel Weber)integral. We expect the advances made here to be useful also in the relativistic case.

Solar flares are one of the most energetic events in the solar system, their impact on Earth at ground level and its atmosphere remains under study. The repercussions of this phenomenon in our technological infrastructure includes radio blackouts and errors in geopositional and navigation systems that are considered natural hazards in ever more countries. Occurrence frequency and intensity of the most energetic solar flares are been taken into account in national programs for civil protection in order to reduce the risk and increase the resilience from Space Weather events. In this work we use the statistical theory of extreme values as well as other statistical methods in order to asses the magnitudes of the most extreme solar flare events expected to occur in a given period of time. We found that the data set under study presents a dual tail behaviour. Our results show that on average we can expect one solar flare greater than X23 each 25 years, that is to say, one such event each two solar cycles.