oalib
Search Results: 1 - 10 of 100 matches for " "
All listed articles are free for downloading (OA Articles)
Page 1 /100
Display every page Item
Moderate deviations and law of the iterated logarithm for intersections of the ranges of random walks  [PDF]
Xia Chen
Mathematics , 2005, DOI: 10.1214/009117905000000035
Abstract: Let S_1(n),...,S_p(n) be independent symmetric random walks in Z^d. We establish moderate deviations and law of the iterated logarithm for the intersection of the ranges #{S_1[0,n]\cap... \cap S_p[0,n]} in the case d=2, p\ge 2 and the case d=3, p=2.
Large deviations and laws of the iterated logarithm for the local times of additive stable processes  [PDF]
Xia Chen
Mathematics , 2006, DOI: 10.1214/009117906000000601
Abstract: We study the upper tail behaviors of the local times of the additive stable processes. Let $X_1(t),...,X_p(t)$ be independent, d-dimensional symmetric stable processes with stable index $0<\alpha\le 2$ and consider the additive stable process $\bar{X}(t_1,...,t_p)=X_1(t_1)+... +X_p(t_p)$. Under the condition $d<\alpha p$, we obtain a precise form of the large deviation principle for the local time \[\eta^x([0,t]^p)=\int_0^t...\int_0^t\delta_x\bigl(X_1(s_1)+... +X_p(s_p)\bigr) ds_1... ds_p\] of the multiparameter process $\bar{X}(t_1,...,t_p)$, and for its supremum norm $\sup_{x\in\mathbb{R}^d}\eta^x([0,t]^p)$. Our results apply to the law of the iterated logarithm and our approach is based on Fourier analysis, moment computation and time exponentiation.
Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks  [PDF]
Richard F. Bass,Xia Chen,Jay Rosen
Mathematics , 2005,
Abstract: Let B_n be the number of self-intersections of a symmetric random walk with finite second moments in the integer planar lattice. We obtain moderate deviation estimates for B_n - E B_n and E B_n- B_n, which are given in terms of the best constant of a certain Gagliardo-Nirenberg inequality. We also prove the corresponding laws of the iterated logarithm.
The law of the iterated logarithm for additive functionals of Markov chains  [PDF]
Yu Miao,Guangyu Yang
Mathematics , 2007,
Abstract: In the paper, the law of the iterated logarithm for additive functionals of Markov chains is obtained under some weak conditions, which are weaker than the conditions of invariance principle of additive functionals of Markov chains in M. Maxwell and M. Woodroofe (2000). The main technique is the martingale argument and the theory of fractional coboundaries.
Moderate deviations and Strassen's law for additive processes  [PDF]
Franziska Kühn,René L. Schilling
Mathematics , 2014, DOI: 10.1007/s10959-014-0584-6
Abstract: We establish a moderate deviation principle for processes with independent increments under certain growth conditions for the characteristics of the process. Using this moderate deviation principle, we give a new proof for Strassen's functional law of the iterated logarithm. In particular, we show that any square-integrable L\'evy process satisfies Strassen's law.
An invariance principle for the law of the iterated logarithm for additive functionals of Markov chains  [PDF]
Guangyu Yang,Yu Miao
Mathematics , 2006,
Abstract: In this paper, we prove Strassen's strong invariance principle for a vector-valued additive functionals of a Markov chain via the martingale argument and the theory of fractional coboundaries. The hypothesis is a moment bound on the resolvent.
Self-normalized moderate deviation and laws of the iterated logarithm under G-expectation  [PDF]
Li-Xin Zhang
Mathematics , 2015,
Abstract: The sub-linear expectation or called G-expectation is a nonlinear expectation having advantage of modeling non-additive probability problems and the volatility uncertainty in finance. Let $\{X_n;n\ge 1\}$ be a sequence of independent random variables in a sub-linear expectation space $(\Omega, \mathscr{H}, \widehat{\mathbb E})$. Denote $S_n=\sum_{k=1}^n X_k$ and $V_n^2=\sum_{k=1}^n X_k^2$. In this paper, a moderate deviation for self-normalized sums, that is, the asymptotic capacity of the event $\{S_n/V_n \ge x_n \}$ for $x_n=o(\sqrt{n})$, is found both for identically distributed random variables and independent but not necessarily identically distributed random variables. As an applications, the self-normalized laws of the iterated logarithm are obtained.
General Large Deviations and Functional Iterated Logarithm Law for Multivalued Stochastic Differential Equations  [PDF]
Jiagang Ren,Jing Wu,Hua Zhang
Mathematics , 2015,
Abstract: In this paper, we prove a large deviation principle of Freidlin-Wentzell's type for the multivalued stochastic differential equations. As an application, we derive a functional iterated logarithm law for the solutions of multivalued stochastic differential equations.
Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm  [PDF]
Richard F. Bass,Xia Chen
Mathematics , 2005, DOI: 10.1214/009117904000000504
Abstract: If \beta_t is renormalized self-intersection local time for planar Brownian motion, we characterize when Ee^{\gamma\beta_1} is finite or infinite in terms of the best constant of a Gagliardo-Nirenberg inequality. We prove large deviation estimates for \beta_1 and -\beta_1. We establish lim sup and lim inf laws of the iterated logarithm for \beta_t as t\to\infty.
Local Strassen''s Law of the Iterated Logarithm for Diffusion Processes in H
扩散过程在Holder范数下的局部 Strassen重对数律

Liu Yonghong,Gao Fuqing,
刘永宏
,高付清

数学物理学报(A辑) , 2006,
Abstract: In this paper, the authors obtain the functional law of the iterated logarithm for diffusion processes by large deviations in Holder norm. As an application, the authors obtain the functional law of the iterated logarithm for iterated Ito integrals.
Page 1 /100
Display every page Item


Home
Copyright © 2008-2017 Open Access Library. All rights reserved.