Large Deviations for the Emprirical Measures of Reflecting Brownian Motion and Related Constrained Processes in $R_+$

Amarjit Budhiraja, Paul Dupuis

Type: Article

Publication Date: 2003-01-01

Citations: 11

DOI: https://doi.org/10.1214/ejp.v8-154

Abstract

We consider the large deviations properties of the empirical measure for one dimensional constrained processes, such as reflecting Brownian motion, the M/M/1 queue, and discrete time analogues. Because these processes do not satisfy the strong stability assumptions that are usually assumed when studying the empirical measure, there is significant probability (from the perspective of large deviations) that the empirical measure charges the point at infinity. We prove the large deviation principle and identify the rate function for the empirical measure for these processes. No assumption of any kind is made with regard to the stability of the underlying process.

Locations

Electronic Journal of Probability - View - PDF

Similar Works

Action	Title	Year	Authors
+	Large Deviations for the Emprirical Measures of Reflecting Brownian Motion and Related Constrained Processes in $R_+$	2003	Aro Nsf
+	Large deviations for subordinated Brownian motion and applications	2014	Janusz Gajda Marcin Magdziarz
+ PDF Chat	A Note on the Large Deviation Principle for Discrete Associated Random Variables	2015	Przemysław Matuła Maciej Ziemba
+	Sample-path large deviations for unbounded additive functionals of the reflected random walk	2020	Mihail Bazhba José Blanchet Chang-Han Rhee Bert Zwart
+	Moderately large deviation principles for the trajectories of random walks and processes with independent increments	2020	А. А. Боровков Vladimir V. Ulyanov Mikhail Zhitlukhin
+	Large deviations for moving average processes	1995	Tiefeng Jiang Marepalli B. Rao Xiangchen Wang
+ PDF Chat	The large deviation principle for stochastic processes. II	2003	Miguel A. Arcones Miguel A. Arcones
+	Sharp large deviations for the log-likelihood ratio of an -Brownian bridge	2013	Shoujiang Zhao Yanping Zhou
+	Large deviations for the empirical mean of an $$M/M/1$$ queue	2013	José Blanchet Peter W. Glynn Sean Meyn
+	The large deviation principle for a compound Poisson process	2017	A. A. Mogulskiĭ
+	Large deviations of stochastic systems and applications	2012	Qi He
+	Large deviations for Markov processes on infinite-dimensional spaces	1985
+	Conditional moderately large deviation principles for the trajectories of random walks and processes with independent increments	2015	А. А. Боровков A. A. Mogulskiĭ
+	Large deviations for martingales with exponential condition	2011	Xiequan Fan Ion Grama Quansheng Liu
+	A Moderate Deviation Principle for m-Dependent Random Variables with Unbounded m	2008	Yu Miao Guangyu Yang
+	Moderately Large Deviation Principles for the Trajectories of Random Walks and Processes with Independent Increments	2014	А. А. Боровков A. A. Mogulskiĭ
+	Large Deviation Property and Asymptotics of Integrals	1985	Richard S. Ellis
+	Large deviation for a class of current-valued processes	1992	Shojiro Manabe
+	A Large Deviation Principle for Stochastic Integrals	2007	Jorge Mendoza García
+	Large deviation principle for Reflected Stochastic Differential Equations driven by G-Brownian motion in non-convex domains	2022	Abdoulaye Soumana Hima Ibrahim Dakaou

Works That Cite This (10)

Action	Title	Year	Authors
+	<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msup></mml:math>-independence of spectral bounds of Schrödinger type semigroups	2007	Masayoshi Takeda
+	Large deviations for the empirical measure of a diffusion via weak convergence methods	2017	Paul Dupuis David Lipshutz
+ PDF Chat	Large deviations of currents in diffusions with reflective boundaries	2021	Emil Mallmin Johan du Buisson Hugo Touchette
+	Lp -independence of spectral bounds of non-local Feynman-Kac semigroups	2009	Masayoshi Takeda Yoshihiro Tawara
+ PDF Chat	Spectral theory and limit theorems for geometrically ergodic Markov processes	2003	Ioannis Kontoyiannis Sean Meyn
+ PDF Chat	Hidden Geometry of Bidirectional Grid-Constrained Stochastic Processes	2021	Aldo Taranto Shahjahan Khan
+ PDF Chat	Large Deviations for Additive Functionals of Reflected Jump-Diffusions	2022	Lea Popovic Giovanni Zoroddu
+ PDF Chat	Dynamical large deviations of reflected diffusions	2020	Johan du Buisson Hugo Touchette
+	Bi-Directional Grid Constrained Stochastic Processes' Link to Multi-Skew Brownian Motion	2021	Aldo Taranto Ron Addie Shahjahan Khan
+	Hidden Geometry of Bi-Directional Grid Constrained Stochastic Processes	2021	Aldo Taranto Shahjahan Khan

Works Cited by This (6)

Action	Title	Year	Authors
+ PDF Chat	A Lower Bound of the Asymptotic Behavior of Some Markov Processes	1982	Tzuu-Shuh Chiang
+ PDF Chat	Large Deviation Lower Bounds for Additive Functionals of Markov Processes	1990	Naresh C. Jain
+	Large deviations for empirical measures of Markov chains	1990	A. de Acosta
+ PDF Chat	Markov Additive Processes I. Eigenvalue Properties and Limit Theorems	1987	Peter Ney Esa Nummelin
+ PDF Chat	Convergence of Probability Measures	1999	Patrick Billingsley
+	Asymptotic evaluation of certain Markov process expectations for large time—III	1976	M. D. Donsker S. R. S. Varadhan