1 citations · 1 across the 8 of their papers we have counts for
9 papers
Probabilistic representation and classical solutions of wave equations with complex polynomial nonlinearities
Joshua J. Y. Chan, Nicolas Privault
We review the probabilistic representation of solutions of wave equations with polynomial nonlinearities in spatial dimensions d=1,2,3 using stochastic branching processes. Under r…
Mixing rates for linear operators under infinitely divisible measures on Banach spaces
Camille Mau, Nicolas Privault
We derive rates of convergence for the mixing of operators under infinitely divisible measures in the framework of linear dynamics on Banach spaces. Our approach is based on the ch…
Gaussian fluctuations of generalized -statistics and subgraph counting in the binomial random-connection model
Qingwei Liu, Nicolas Privault
We derive normal approximation bounds for generalized -statistics of the form \begin{equation*} S_{n,k}(f):=\sum_{ 1 \leq β(1),\dots,β(k) \leq n \atop β(i)\neβ(j), \ 1\leq i\ne…
Stability analysis of a branching diffusion solver for semilinear heat equations
Qiao Huang, Nicolas Privault
Stochastic branching algorithms provide a useful alternative to grid-based schemes for the numerical solution of partial differential equations, particularly in high-dimensional se…
Probabilistic representation of ODE solutions with quantitative estimates
Qiao Huang, Nicolas Privault
This paper considers the probabilistic representation of the solutions of ordinary differential equations (ODEs) by the generation of marked random trees in which marks can be inte…
Binary Galton-Watson trees with mutations
Qiao Huang, Nicolas Privault
We consider a multitype Galton-Watson process that allows for the mutation and reversion of individual types in discrete and continuous time. In this setting, we explicitly compute…
Normal to Poisson phase transition for subgraph counting in the random-connection model
Qingwei Liu, Nicolas Privault
We consider the limiting behavior of the count of subgraphs isomorphic to a graph with fixed endpoints (or roots) in the random-connection model, as the intensity …
On the random generation of Butcher trees
Qiao Huang, Nicolas Privault
The main goal of this paper is to provide an algorithm for the random sampling of Butcher trees and the probabilistic numerical solution of ordinary differential equations (ODEs).…
Graph connectivity with fixed endpoints in the random-connection model
Qingwei Liu, Nicolas Privault
We consider the count of subgraphs with an arbitrary configuration of endpoints in the random-connection model based on a Poisson point process on . We present combinat…