Large Deviations for Stochastic Processes

By Jin Feng, Thomas G. Kurtz. 2006

506 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/33648b1128495a93ac0308d87ff1cb943fe71135

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. Wei Liu
2. A. Budhiraja
3. Paul Dupuis
4. Xicheng Zhang
5. Michael Röckner
6. Annie Millet
7. Jiagang Ren
8. Tusheng Zhang

In Mathematical Physics

1. Xicheng Zhang
2. Wei Liu
3. Annie Millet
4. A. Budhiraja
5. Paul Dupuis
6. Jinqiao Duan
7. Anatolii A. Puhalskii
8. Jiagang Ren

Citations in the corpus

• On large deviations of coupled diffusions with time scale separation (2013, background): “slow process, this sort of result is usually referred to as “the averaging principle;” for contributions, see Freı̆dlin [17], Veretennikov [51, 53, 58, 59], Feng and Kurtz [16], Section 11, and references therein.”
• Freidlin-Wentzell's Large Deviations for Stochastic Evolution Equations (2008, methodology): “In [ 12 ], the approach for LDP is based on nonlinear semigroup and infinite dimensional”
• Ergodic Markov processes and Poisson equations (lecture notes) (2016, background): “However, this simple result does not pretend to be even an introduction to large deviations, about which theory see [5, 7, 13, 14, 17, 36, 42], et al.”
• Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise (2008, methodology): “An alternative approach for LDP has been developed by Feng and Krutz in [17], which mainly used nonlinear semigroup theory and infinite dimensional Hamilton-Jacobi equation.”
• On the Relation between Gradient Flows and the Large-Deviation Principle, with Applications to Markov Chains and Diffusion (2013, unknown): “The other method, due to Feng and Kurtz [FK06], provides a formal way to calculate the large-deviation rate directly, although it requires more advanced techniques to make the arguments rigorous.”
• Large Deviations Asymptotics and the Spectral Theory of Multiplicatively Regular Markov Processes (2005, unknown): “24”
• Large deviations for the Boussinesq equations under random influences (2008, methodology): “An alternative approach [11] for large deviations is based on nonlinear semi-group theory and infinite-dimensional Hamilton-Jacobi equations, and it also requires establishing exponential tightness.”
• Metric viscosity solutions of Hamilton–Jacobi equations depending on local slopes (2015, methodology): “equations in the Wasserstein space have been proposed, see [1, 16, 17, 30, 31, 32, 33, 34, 36, 47, 52] and also a short discussion about them in the introduction of [37].”
• Large deviation properties of weakly interacting processes via weak convergence methods (2010, background): “A proof of the large deviation principle for systems with constant diffusion coefficient that is based on a comparison result for a related infinite-dimensional Hamilton–Jacobi– Bellman equation appears in [17], Section 13.”
• SMALL-TIME ASYMPTOTICS FOR FAST MEAN-REVERTING STOCHASTIC VOLATILITY MODELS (2010, methodology): “We adapt methods developed in Feng and Kurtz [13].”