Large deviations for infinite dimensional stochastic dynamical systems

By A. Budhiraja, Paul Dupuis, Vasileios Maroulas. 2008

277 citations recorded by the source corpus.

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 the process state is infinite dimensional. In this paper we show how such approximations can be avoided for a variety of infinite dimensional models driven by some form of Brownian noise. The approach is based on a variational representation for functionals of Brownian motion. Proofs of large deviations properties are reduced to demonstrating basic qualitative properties (existence, uniqueness and tightness) of certain perturbations of the original process.

Subfields: Finance, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8d05e0a36eb17362ec3d8acaafb39022abc7a2b1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Tusheng Zhang
2. Xicheng Zhang
3. A. Budhiraja
4. Paul Dupuis
5. Jiang Chen
6. Jiagang Ren
7. Jianliang Zhai
8. Wei Liu

In Statistical and Nonlinear Physics

1. Tusheng Zhang
2. Xicheng Zhang
3. Paul Dupuis
4. A. Budhiraja
5. Jiang Chen
6. Jianliang Zhai
7. Jiagang Ren
8. Wei Liu

In Statistics and Probability

1. Tusheng Zhang
2. Xicheng Zhang
3. Jiagang Ren
4. Tiange Xu
5. A. Budhiraja
6. Paul Dupuis
7. Jiang Chen
8. Jianliang Zhai

Citations in the corpus

• Large Deviations for Stochastic Partial Differential Equations Driven by a Poisson Random Measure (2012, methodology): “In recent years an approach based on certain variational representation formulas for moments of nonnegative functionals of Brownian motions [7] has been increasingly used for the study of the small noise large deviation problem for Brownian motion driven infinite dimensional systems [2, 7, 8, 10, 13”
• Freidlin-Wentzell's Large Deviations for Stochastic Evolution Equations (2008, methodology): “Laplace Principle, Freidlin-Wentzell’s Large Deviation, Stochastic Evolution Equation, Variational Representation Formula.”
• Variational representations for continuous time processes (2011, background): “Previous work on variational representations has focused on either discrete time processes [11], functionals of finite-dimensional Brownian motion [2], or various formulations of infinite-dimensional Brownian motion [4,6].”
• Moderate Deviation Principles for Stochastic Differential Equations with Jumps (2014, background): “In [9, 10] a general approach for studying large deviation problems in such settings was introduced that is based on a variational representation for expectations of positive functionals of an infinite-dimensional Brownian motion.”
• White noise driven SPDEs with reflection: Existence, uniqueness and large deviation principles (2009, methodology): “The reader is referred to [1,2,7] for details of this method.”
• Large and Moderate Deviation Principles for McKean-Vlasov SDEs with Jumps (2020, methodology): “Among the approaches to deal with these problems, the weak convergence method based on a variational representation for positive measurable functionals of a BM and/or PRM (see [4, 6, 7, 8, 9]) is proved to be a powerful tool to establish large and moderate deviation principles for various dynamical ”