Explanipedia

Large deviations for empirical measures of self-interacting Markov chains Open

Amarjit Budhiraja, Adam Waterbury, Pavlos Zoubouloglou · 2025

Strong existence, pathwise uniqueness and chains of collisions in infinite Brownian particle systems Open

Sayan Banerjee, Amarjit Budhiraja, Peter Rudzis · 2025

We study strong existence and pathwise uniqueness for a class of infinite-dimensional singular stochastic differential equations (SDE), with state space as the cone $\{x \in \mathbb{R}^{\mathbb{N}}: -\infty < x_1 \leq x_2 \leq \cdots\}$, r…

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Open

Shankar Bhamidi, Amarjit Budhiraja, Akshay Sakanaveeti · 2024

We study inhomogeneous random graphs with a finite type space. For a natural generalization of the model as a dynamic network-valued process, the paper establishes the following results: (a) Functional central limit theorems for the infini…

Flocking under Fast and Large Jumps: Stability, Chaos, and Traveling Waves Open

Sayan Banerjee, Amarjit Budhiraja, Dilshad Imon · 2024

We study a model for flocking given by a $n$-particle system under which each particle jumps forward by a random amount, independently sampled from a given distribution $θ$, with rate given by a non-increasing function $w$ of its signed di…

Diffusion limits in the quarter plane and non-semimartingale reflected Brownian motion Open

Rami Atar, Amarjit Budhiraja · 2024

We consider a continuous-time random walk in the quarter plane for which the transition intensities are constant on each of the four faces $(0,\infty)^2$, $F_1=\{0\}\times(0,\infty)$, $F_2=(0,\infty)\times\{0\}$ and $\{(0,0)\}$. We show th…

Large deviations for small noise diffusions over long time Open

Amarjit Budhiraja, Pavlos Zoubouloglou · 2024

We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers (L…

Large deviations for small noise diffusions over long time Open

Amarjit Budhiraja, Pavlos Zoubouloglou · 2024

We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers (L…

Ergodic Control of Resource Sharing Networks: Lower Bound on Asymptotic Costs Open

Amarjit Budhiraja, Michael Conroy, Dane Johnson · 2023

Dynamic capacity allocation control for resource sharing networks (RSN) is studied when the networks are in heavy traffic. The goal is to minimize an ergodic cost with a linear holding cost function. Our main result shows that the optimal …

Simple Form Control Policies for Resource Sharing Networks with HGI Performance Open

Amarjit Budhiraja, D. N. Johnson · 2023

We consider a family of resource sharing networks, known as bandwidth sharing models, in heavy traffic with general service and interarrival times. These networks, introduced in Massoulie and Roberts (2000) as models for internet flows, ha…

Fluctuations of the Atlas model from inhomogeneous stationary profiles Open

Sayan Banerjee, Amarjit Budhiraja, Peter Rudzis · 2023

The infinite Atlas model describes the evolution of a countable collection of Brownian particles on the real line, where the lowest particle is given a drift of $γ\in [0,\infty)$. We study equilibrium fluctuations for the Atlas model when …

Large Deviations for Empirical Measures of Self-Interacting Markov Chains Open

Amarjit Budhiraja, Adam Waterbury, Pavlos Zoubouloglou · 2023

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 $\{X_n, \; n \in \mathbb{N}_0\}$ of $Δ^o$-valued random variables su…

Load Balancing in Parallel Queues and Rank-based Diffusions Open

Sayan Banerjee, Amarjit Budhiraja, Benjamin Estevez · 2023

Consider a system with $K$ parallel queues in which the server for each queue processes jobs at rate $n$ and the total arrival rate to the system is $nK-\upsilon \sqrt{n}$ where $\upsilon \in (0, \infty)$ and $n$ is large. We study rank-ba…

The Inert Drift Atlas Model Open

Sayan Banerjee, Amarjit Budhiraja, Benjamin Estevez · 2022

Long Time Behavior of Finite and Infinite Dimensional Reflected Brownian Motions Open

Sayan Banerjee, Amarjit Budhiraja · 2022

This article presents a review of some old and new results on the long time behavior of reflected diffusions. First, we present a summary of prior results on construction, ergodicity and geometric ergodicity of reflected diffusions in the …

Extremal Invariant Distributions of Infinite Brownian Particle Systems with Rank Dependent Drifts Open

Sayan Banerjee, Amarjit Budhiraja · 2022

\noindent Consider an infinite collection of particles on the real line moving according to independent Brownian motions and such that the $i$-th particle from the left gets the drift $g_{i-1}$. The case where $g_0=1$ and $g_{i}=0$ for all…

Large Deviations for Small Noise Diffusions Over Long Time Open

Amarjit Budhiraja, Pavlos Zoubouloglou · 2022

We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers (L…

Empirical Measure Large Deviations for Reinforced Chains on Finite Spaces Open

Amarjit Budhiraja, Adam Waterbury · 2022

Let $A$ be a transition probability kernel on a finite state space $Δ^o =\{1, \ldots , d\}$ such that $A(x,y)>0$ for all $x,y \in Δ^o$. Consider a reinforced chain given as a sequence $\{X_n, \; n \in \mathbb{N}_0\}$ of $Δ^o$-valued random…

Approximating quasi-stationary distributions with interacting reinforced random walks Open

Amarjit Budhiraja, Nicolás Fraiman, Adam Waterbury · 2021

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 certain interacting chains in which the interaction is give…

Does Momentum Help? A Sample Complexity Analysis Open

Gugan Thoppe, Rohan Deb, Swetha Ganesh, Amarjit Budhiraja · 2021

Momentum methods are popularly used in accelerating stochastic iterative methods. Although a fair amount of literature is dedicated to momentum in stochastic optimisation, there are limited results that quantify the benefits of using heavy…

Does Momentum Help? A Sample Complexity Analysis Open

Swetha Ganesh, Rohan Deb, Gugan Thoppe, Amarjit Budhiraja · 2021

Stochastic Heavy Ball (SHB) and Nesterov's Accelerated Stochastic Gradient (ASG) are popular momentum methods in stochastic optimization. While benefits of such acceleration ideas in deterministic settings are well understood, their advant…

Long Time Results for a Weakly Interacting Particle System in Discrete Time Open

Amarjit Budhiraja, Abhishek Pal Majumder · 2021

We study long time behavior of a discrete time weakly interacting particle system, and the corresponding nonlinear Markov process in Rd, described in terms of a general stochastic evolution equation. In a setting where the state space of t…

Stationary Distribution Convergence for Generalized Jackson Networks in Heavy Traffic Open

Amarjit Budhiraja, Chihoon Lee · 2021

In a recent paper [5] it was shown that under suitable conditions stationary distributions of the (scaled) queue lengths process for a generalized Jackson network converge to the stationary distribution of the associated re ected Brownian …

Large deviations for infinite dimensional stochastic dynamical systems Open

Amarjit Budhiraja, Paul Dupuis, Vasileios Maroulas · 2021

The large deviations analysis of solutions to stochastic differential equations and related processes is often based on approximation. The construction and justification of the approximations can be onerous, especially in the case where th…

Convergent Numerical Scheme for Singular Stochastic Control with State Constraints in a Portfolio Selection Problem Open

Amarjit Budhiraja, Kevin J. Ross · 2021

We consider a singular stochastic control problem with state constraints that arises in problems of optimal consumption and investment under transaction costs. Numerical approximations for the value function using the Markov chain approxim…

Approximation and Limit Results for Nonlinear Filters Over an Infinite Time Interval: Part II, Random Sampling Algorithms Open

Amarjit Budhiraja, Harold J. Kushner · 2021

The paper is concerned with approximations to nonlinear filtering problems that are of interest over a very long time interval. Since the optimal filter can rarely be constructed, one needs to compute with numerically feasible approximatio…

Action Time Sharing Policies for Ergodic Control of Markov Chains Open

Amarjit Budhiraja, Xin Liu, Adam Shwartz · 2021

Ergodic Rate Control Problem for Single Class Queueing Networks Open

Amarjit Budhiraja, Arka P. Ghoshp, Chihoon Lee · 2021

We consider critically loaded single class queueing networks with infinite buffers in which arrival and service rates are state (i.e., queue length) dependent and may be dynamically controlled. An optimal rate control problem for such netw…

Limits of relative entropies associated with weakly interacting particle systems Open

Amarjit Budhiraja, Paul Dupuis, Markus Fischer, Kavita Ramanan · 2021

The limits of scaled relative entropies between probability distributions associated with $N$-particle weakly interacting Markov processes are considered. The convergence of such scaled relative entropies is established in various settings…

Large deviations for stochastic partial differential equations driven by a Poisson random measure Open

Amarjit Budhiraja, Chen Jiang, Paul Dupuis · 2021

Stochastic partial differential equations driven by Poisson random measures (PRMs) have been proposed as models for many different physical systems, where they are viewed as a refinement of a corresponding noiseless partial differential eq…

Some Large Deviations Asymptotics in Small Noise Filtering Problems Open

Anugu Sumith Reddy, Amarjit Budhiraja, Amit Apte · 2021

We consider nonlinear filters for diffusion processes when the observation and signal noises are small and of the same order. As the noise intensities approach zero, the nonlinear filter can be approximated by a certain variational problem…

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