Adam Waterbury

activity

20192026

collaborators

6 papers

stat.ME2026

RKHS-Based Inference for Nonlinear Granger Causality via Conditional Centering

Yuhan Tian, Adam Waterbury, Marie-Christine Düker

Granger causality is commonly formulated through linear prediction in vector autoregressive models, limiting its ability to detect nonlinear predictive relationships. We propose a…

math.ST2025

Kernel Estimation for Nonlinear Dynamics

Marie-Christine Düker, Adam Waterbury

Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis o…

math.PR2023

Large Deviations for Empirical Measures of Self-Interacting Markov Chains

Amarjit Budhiraja, Adam Waterbury, Pavlos Zoubouloglou

Let $Δ^{o}$ be a finite set and, for each probability measure $m$ on $Δ^{o}$ , let $G (m)$ be a transition probability kernel on $Δ^{o}$ . Fix $x_{0} \in Δ^{o}$ and consider the chain $\{X_n, \…

math.PR2022

Empirical Measure Large Deviations for Reinforced Chains on Finite Spaces

Amarjit Budhiraja, Adam Waterbury

Let $A$ be a transition probability kernel on a finite state space $Δ^{o} = {1, \dots, d}$ such that $A (x, y) > 0$ for all $x, y \in Δ^{o}$ . Consider a reinforced chain given as a seque…

math.PR2020

Approximating Quasi-Stationary Distributions with Interacting Reinforced Random Walks

Amarjit Budhiraja, Nicolas Fraiman, Adam Waterbury

We propose two numerical schemes for approximating quasi-stationary distributions (QSD) of finite state Markov chains with absorbing states. Both schemes are described in terms of…

math.PR2019

Asymptotics of Quasi-Stationary Distributions of Small Noise Stochastic Dynamical Systems in Unbounded Domains

Amarjit Budhiraja, Nicolas Fraiman, Adam Waterbury

We consider a collection of Markov chains that model the evolution of multitype biological populations. The state space of the chains is the positive orthant, and the boundary of t…