We design exact polynomial expansions of a class of Feynmanâ€“ Kac particle distributions. These expansions are finite and are parametrized by coalescent trees and other related combinatorialâ€¦ (More)

We design a theoretic tree-based functional representation of a class of Feynman-Kac particle distributions, including an extension of the Wick product formula to interacting particle systems. Theseâ€¦ (More)

We here investigate the well-posedness of a networked integrate-andfire model describing an infinite population of neurons which interact with one another through their common statisticalâ€¦ (More)

Building on the work of Schweizer (1995) and ÄŒernÃ½ and Kallsen (2007), we present discrete time formulas minimizing the mean square hedging error for multidimensional assets. In particular, we giveâ€¦ (More)

This article considers the problem of storing the paths generated by a particle filter and more generally by a sequential Monte Carlo algorithm. It provides a theoretical result bounding the expectedâ€¦ (More)

This article is concerned with the long time behavior of neutral genetic population models, with fixed population size. We design an explicit, finite, exact, genealogical tree based representation ofâ€¦ (More)

Motivated by some applications in neurosciences, we here collect several estimates for the density of the first hitting time of a threshold by a nonhomogeneous one-dimensional diffusion process andâ€¦ (More)

We present a mean field particle theory for the numerical approximation of Feynman-Kac path integrals in the context of nonlinear filtering. We show that the conditional distribution of the signalâ€¦ (More)

It can be shown that when the payoff function is convex and decreasing (respectively increasing) with respect to the underlying (multidimensional) assets, then the same is true for the value of theâ€¦ (More)

Several particle algorithms admit a Feynman-Kac representation such that the potential function may be expressed as a recursive function which depends on the complete state trajectory. An importantâ€¦ (More)