The classical Feynman–Kac identity builds a bridge between stochastic analysis and partial differential equations (PDEs) by providing representations for solutions of linear Kolmogorov PDEs. This opens the door derivation sampling based Monte Carlo approximation methods, which can be meshfree thereby stand chance to approximate PDEs without suffering from curse dimensionality. In this paper, we...

The growth-fragmentation equation models systems of particles that grow and reproduce as time passes. An important question concerns the asymptotic behaviour its solutions. Bertoin Watson (2018) developed a probabilistic approach relying on Feynman-Kac formula, enabled them to answer this for sublinear growth rates. This assumption ensures microscopic remain microscopic. In work, we go further ...

We study algorithms for approximation of Feynman-Kac path integrals in the worst case setting. The algorithms use a nite number of samples of the initial condition and potential functions. We present a new algorithm and an explicit bound on its cost to compute an "-approximation to the Feynman-Kac path integral. We also establish bounds on the worst case complexity of Feynman-Kac path integrati...

We study the lengths of the cycles formed by trajectories in the Feynman-Kac representation of the Bose gas. We discuss the occurrence of infinite cycles and their relation to Bose-Einstein condensation.

We consider Gibbs measures relative to Brownian motion of Feynman-Kac type, with single site potential V . We show that for a large class of V , including the Coulomb potential, there exist infinitely many infinite volume Gibbs measures.

Using the high moment method and the Feynman-Kac semigroup technique, we obtain moderate deviations and laws of the iterated logarithm for the volume of the intersections of two and three dimensional Wiener sausages.