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math.PR2025

The dual Burnside process

Ivan Z. Feng

The Burnside process is a classical Markov chain for sampling uniformly from group orbits. We give a systematic study of the dual Burnside process, obtained by interchanging the ro…

math.PR2024

Concentration and moment inequalities for sums of independent heavy-tailed random matrices

Moritz Jirak, Stanislav Minsker, Yiqiu Shen +1

We prove Fuk-Nagaev and Rosenthal-type inequalities for sums of independent random matrices, focusing on the situation when the norms of the matrices possess finite moments of only…

math.PR2023

Set-valued stochastic integrals for convoluted Lévy processes

Weixuan Xia

In this paper we study set-valued Volterra-type stochastic integrals driven by Lévy processes. Upon extending the classical definitions of set-valued stochastic integral functional…

math.PR2022★ 4 cited

From finite population optimal stopping to mean field optimal stopping

Mehdi Talbi, Nizar Touzi, Jianfeng Zhang

This paper analyzes the convergence of the finite population optimal stopping problem towards the corresponding mean field limit. Building on the viscosity solution characterizatio…

math.PR2022★ 1 cited

Zero Bias Enhanced Stein Couplings

Larry Goldstein

The Stein couplings of Chen and Roellin (2010) vastly expanded the range of applications for which coupling constructions in Stein's method for normal approximation could be applie…

math.PR2022★ 9 cited

Random walk on nonnegative integers in beta distributed random environment

Guillaume Barraquand, Mark Rychnovsky

We consider random walks on the nonnegative integers in a space-time dependent random environment. We assume that transition probabilities are given by independent $\mathrm{Beta}(μ…

math.PR2020★ 6 cited

Three Candidate Plurality is Stablest for Small Correlations

Steven Heilman, Alex Tarter

Using the calculus of variations, we prove the following structure theorem for noise stable partitions: a partition of -dimensional Euclidean space into disjoint sets of fix…

math.PR2020★ 3 cited

Non-Stationary Queues with Batch Arrivals

Andrew Daw, Brian Fralix, Jamol Pender

Motivated by applications that involve setting proper staffing levels for multi-server queueing systems with batch arrivals, we present a thorough study of the queue-length process…

math.PR2020★ 1 cited

Set-Valued Backward Stochastic Differential Equations

Çağın Ararat, Jin Ma, Wenqian Wu

In this paper, we establish an analytic framework for studying set-valued backward stochastic differential equations (set-valued BSDE), motivated largely by the current studies of…

math.PR2020★ 34 cited

Matching Queues with Reneging: a Product Form Solution

Francisco Castro, Hamid Nazerzadeh, Chiwei Yan

Motivated by growing applications in two-sided markets, we study a parallel matching queue with reneging. Demand and supply units arrive to the system and are matched in an FCFS ma…

math.PR2019

On Optimal Dividend and Investment Strategy under Renewal Risk Models

Lihua Bai, Jin Ma

In this paper we continue investigating the optimal dividend and investment problems under the Sparre Andersen model. More precisely, we assume that the claim frequency is a renewa…

math.PR2019★ 2 cited

Density of the signature process of fBm

Fabrice Baudoin, Qi Feng, Cheng Ouyang

We study the density of the signature of fractional Brownian motions with parameter . In particular, we prove existence, smoothness, global Gaussian upper bounds and Varadha…

math.PR2018★ 2 cited

An Ephemerally Self-Exciting Point Process

Andrew Daw, Jamol Pender

Across a wide variety of applications, the self-exciting Hawkes process has been used to model phenomena in which the history of events influences future occurrences. However, ther…

math.PR2018★ 10 cited

Viscosity Solutions to Parabolic Master Equations and McKean-Vlasov SDEs with Closed-loop Controls

Cong Wu, Jianfeng Zhang

The master equation is a type of PDE whose state variable involves the distribution of certain underlying state process. It is a powerful tool for studying the limit behavior of la…

math.PR2018

On an alternative sequence comparison statistic of Steele

Ümit Işlak, Alperen Y. Özdemir

The purpose of this paper is to study a statistic that is used to compare the similarity between two strings, which is first introduced by Michael Steele in 1982. It was proposed a…

math.PR2018

Moment inequalities for matrix-valued U-statistics of order 2

Stanislav Minsker, Xiaohan Wei

We present Rosenthal-type moment inequalities for matrix-valued U-statistics of order 2. As a corollary, we obtain new matrix concentration inequalities for U-statistics. One of ou…

math.PR2017★ 3 cited

A Martingale Approach for Fractional Brownian Motions and Related Path Dependent PDEs

Frederi Viens, Jianfeng Zhang

In this paper we study dynamic backward problems, with the computation of conditional expectations as a main objective, in a framework where the (forward) state process satisfies a…

math.PR2017★ 2 cited

Stochastic Control with Delayed Information and Related Nonlinear Master Equation

Yuri F. Saporito, Jianfeng Zhang

In this paper we study stochastic control problems with delayed information, that is, the control at time can depend only on the information observed before time for some…

math.PR2017★ 4 cited

Stein's method for negatively associated random variables with applications to second order stationary random fields

Nathakhun Wiroonsri

Let be a negatively associated mean zero random vector with components that obey the bound , and whose sum $W = \sum_{i=1…

math.PR2017★ 6 cited

Geodesics Toward Corners in First Passage Percolation

Kenneth S. Alexander, Quentin Berger

For stationary first passage percolation in two dimensions, the existence and uniqueness of semi-infinite geodesics directed in particular directions or sectors has been considered…

math.PR2017★ 7 cited

Stochastic Approximation with Random Step Sizes and Urn Models with Random Replacement Matrices Having Finite Mean

Ujan Gangopadhyay, Krishanu Maulik

Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochast…

math.PR2017

Integration by parts and quasi-invariance for the horizontal Wiener measure on a foliated compact manifold

Fabrice Baudoin, Maria Gordina, Qi Feng

We prove several versions of Driver's integration by parts formula for the horizontal Wiener measure on a totally geodesic Riemannian foliation and prove that the horizontal Wiener…

math.PR2017★ 1 cited

On the Cauchy problem for integro-differential equations in the scale of spaces of generalized smoothness

R. Mikulevicius, C. Phonsom

Parabolic integro-differential model Cauchy problem is considered in the scale of Lp -spaces of functions whose regularity is defined by a scalable Levy measure. Existence and uniq…

math.PR2017

Time-Homogeneous Parabolic Wick-Anderson Model in One Space Dimension: Regularity of Solution

Hyun-Jung Kim, Sergey V Lototsky

Even though the heat equation with random potential is a well-studied object, the particular case of time-independent Gaussian white noise in one space dimension has yet to receive…