極限定理と大偏差原理に関する研究

极限定理与大偏差原理研究

• 批准号: 06640330
• 负责人: 田村 要造
• 金额: $ 1.34万
• 依托单位: Keio University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 无数据
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-06640330/
• 关键词: 大偏差原理; ラプラス近似; 非対称マルコフ過程

本研究の第一の目的は非対称マルコフ過程の大偏差原理のラプラス近似の精密化にあった。これに関してはスイスのBolthausen等と共同して次のような結果を得た。Eをコンパクト空間とし、E上の確立測度の全体をM^+_1とおく。Ωを道の空間、{P_x}_<x∈E>をxを出発するΩ上の時間的に一様なマルコフ過程の推移確率測度とする。T>0に対して経験確立測l_Tをl_T=(1/T)∫^T_0δω(t)dtとおく。M^+_1上の有界連続関数Uに対しラプラス近似Z_<x,t>=P_x[exp(TU(l_t))]の主要項はDonskerとVaradhanの一般論によりrate関数Iを用いてlim_<T→∞>(1/T)logZ_<x,T>=-inf{F(λ);λ∈M^+_1}(=f_0),F(λ)=I(λ)-U(λ)ともとまる。V={v∈M^+_1;F(v)=f_0}とおきμ∈M^+_1が{P_x}_<x∈E>の不変測度とあるとする。{P_x}_<x∈E>に対応するC(E)上の半群を{P_t}_<t>0>とし、generatorをLとする。rate関数Iは一般にはI(λ)=-inf{∫_E(Lu/u)dλ:u∈aDom(L),u>0}と与えられる。ここで「P_tがμに関し正の連続な密度を持つ」と仮定するとVを含むある確率速度の族に対してIがI(λ)=-(l,Lu)_<μ >,λ(dx)=l(x)u(x)μ(dx)と対称過程の場合と類似の形で陽に表せることが示される。またMをE上のsigned mea-sure全体に適当なノルムを入れた空間とし「UはM上滑らか」であると仮定する。ここで更に「FのVでのHessianは非退化である」と仮定する。すると♯V<∞でZ_<x,T>の展開の定数項は次の様に求められる。Z_<x,T>〜exp(-f_0T)Σ_<v∈v>g_v,但しg_v=u_v(x)∫_Eu_v(y)^<-1>v(dy){det_<L2(dv)>(I-D^2U(v)(G^<1/2>_v・,G^<1/2>_v))}^<-1/2>,G_vはvを不変測度に持つUの一階微分から定まるΩ上のマルコフ過程のグリーン作用素。また自己相似過程の極限定理に関しては前島がoperator self similar過程の研究を更にすすめ興味深い例とその極限定理を得た。

The first purpose of this study is to approximate the precision of the large deviation principle of the process. This is the first time that Bolthausen and other people have received good results. Make sure that all the M^ + _ 1 measurements are available on the E-mail and the E-mail. Omega-channel space, {Playx} _ & lt; x ∈ E & gt;, please check the accuracy of the process during the last few hours. Make sure that I _ T _ t _ T = (1) T) ~ (1) ^ T _ 0 δ ω (t) dt I _ T). The number of bounded links on M ^ + _ 1 is similar to the number of bounded links on M ^ + _ 1. The number of bounded links on M ^ + _ 1 is similar to the number of bounded links on M ^ + _ 1. The number of bounded links on M ^ + _ 1 is similar to the number of bounded links on M ^ + _ 1. The number of bounded links on M ^ + _ 1 is similar to the number of bounded links on M ^ + _ 1. The number of bounded links on M ^ + _ 1 is similar to the number of bounded links on M ^ + _ 1. The number of bounded links on M ^ + _ 1 is similar to the number of bounded links on M ^ + _ 1. The number of bounded links on M ^ + _ 1 is similar to the number of bounded links on M ^ + _ 1. The number of bounded links on M ^ + _ 1 is similar to the number of λ ∈ M ^ + 1} (= f = 0), F (λ) = I (λ)-U (λ). V = {v ∈ M ^ + _ 1x F (v) = f (v) = f (v)} F (v) = f (v)} F (v) = F (v) = F (v) {Prisx} _ & lt; x ∈ E & gt; algebra algebra C (E) on the semigroup {Plott} _ & lt;t>0> algebra, generatorLateral algebra. Rate number I general formula I (λ) =-inf {∞ _ E (Lu/u) d λ: u ∈ aDom (L), upright gtterist0} and equal to zero. The density of the positive connection is similar to that of the lt;. I (λ) =-(lline Lu) _ & gt;, λ (dx) = l (x) u (x) μ (dx). It is said that the process is similar. Please contact all the signed mea-sure users on the Internet when they enter the "UBG" space station. Change the number of non-degenerative factors such as FLV, Hessian, etc. Please tell me that Z _ & lt;x,T> is open for a number of times. Zodiac g_v=u_v (x) _ Eu_v (y) ^ & lt;-1>v (dy) {det_<L2 (dv) & gt; (I-D ^ 2U (v) (G ^ & lt;1/2>_v, G ^ & lt;1/2>_v))} ^ & lt;-1/2&gt , GV, v, V, V, Learn from your own similar process limit Theorem, learn from the previous operator self similar process study, make it taste better, for example, you can get the limit Theorem.

项目成果

K.Kawazu: "Localization of one-dimensional random walks in random environment" in Proc. Intern. Conf. on Stock.Processes,Physics & Geometry II ed. by S.Albeverio et al. (発表予定).

K.Kawazu：“随机环境中的一维随机游走”，实习生会议，S.Albeverio 等人。

E.Bolthausen: "Laplace apprax:mations for large devictions of nonreversible Markov processes PartI:The mondegenerate case" Ann.Probab.(発表予定).

E.Bolthausen：“拉普拉斯逼近：不可逆马尔可夫过程的大偏差第一部分：Mondegenerate 案例”Ann.Probab（待提交）。

H.Tanaka: "Localization of a diffusion process in a one-dimensional Brownian environment" Comm.Pure Appl.Math.47. 755-766 (1994)

H.Tanaka：“一维布朗环境中扩散过程的局域化”Comm.Pure Appl.Math.47。

M.Maejima: "Operator-self-similar stable processes" Stoch.Processes Appl.54. 139-163 (1994)

M.Maejima：“算子自相似稳定过程”Stoch.Processes Appl.54。