臺灣博碩士論文加值系統

在這篇文章中，我們研究對稱交互作用粒子系統的大離差行為。
Kipnis, et al.於1994年將導出一般性簡單對稱互斥過程流力極限的行為，本篇文章研究此互斥過程流力極限的大離差行為。

In the present article, we study the large deviation property of the generalized symmetric exclusion process.
Once the hydrodynamic limit, which corresponds to a space-time law of large numbers type result, of a Markov process has been established, a natural step is to consider the large deviations from the limit.
Kipnis, et al. derived the hydrodynamic limit of a generalized symmetric exclusion process, which is a non-gradient system. We then derive the large deviation principle of this model.

口試委員會審定書……………………………………………… i
誌謝………… …………………………………………………… ii
中文摘要………………………………………………… iii
英文摘要…………………………………………………………… iv
1. Introduction ……………………………………………… 1
2. Notation and Results ………………………………… …… 1
3. Upper Bound ………………………………………………… 5
4. Hydrodynamic Limit for a Weakly Perturbed Process …12
5. Lower Bound ……………………………………………………17
參考文獻…………………………………………………………… 19

[1] C, Kipnis, S. Olla, S.R.S Varadhan, Hydrodynamics and large deviations
for simple exclusion process. Comm. Pure Appl. Math., 42
(1989), 115-137.
[2] M.D. Donsker, S.R.S. Varadhan, Large deviations from a hydrodynamic
scaling limit. Comm. Pure Appl. Math., 42 (1989), 243-270.
[3] S.R.S. Varadhan, Nonlinear diffusion limit for a system with nearest
neighbor interations II. Asymptotic Problems in Probability
Theory; Stochastic Models and Diffusions on Fractals. Proceedings
of the Taniguchi Symposium, Sanda and Kyoto (1990), 75-130.
Longman, Essex, England.
[4] J. Quastel, Large Deviations From Hydrodynamic Scaling Limit for
A Non-Gradient System. The Annals of Probability., 23 (1995),
724-742.
[5] C, Kipnis, C. Landim, S. Olla, Hydrodynamical Limit for a Nongradient
System: The Generalized Symmetric Exclusion Process.
Comm. Pure Appl. Math., 47 (1994), 1475-1545.
[6] O. Benois, C. Kipnis, C. Landim, Large deviations from the hydrodynamic
limit of mean zero asymmetric zero range processes.
Stochastic Processes and theire applications., 55 (1995), 65-89.
[7] P. B´enilan, H. Tour´e, Sur l’´equation g´en´erale ut = ϕ(u)xx¡ψ(u)x+
ν.C.R.. Acad. Sci. Paris S´er. 1, 299(18) (1984)
[8] Claude Kipnis, Claudio Landim, Scaling Limits of Interacting Particle
Systems. Springer, (1999)