In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of i...In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of increments. Our results imply the theorem that have been given by Csorgo and Revesz (1978), and some of their conditions are removed.展开更多
In this paper, we prove a theorem on the set of limit points of the increments of a two-parameter Wiener process via establishing a large deviation principle on the increments of the two-parameter Wiener process.
A general form of the increments of two-parameter fractional Wiener process is given. The results of Csoergo-Révész increments are a special case,and it also implies the results of the increments of the two-...A general form of the increments of two-parameter fractional Wiener process is given. The results of Csoergo-Révész increments are a special case,and it also implies the results of the increments of the two-parameter Wiener process.展开更多
In this paper, with the aid of large deviation formulas established in strong topology of functional space generated by HSlder norm, we discuss the functional sample path properties of subsequence＇s C-R increments fo...In this paper, with the aid of large deviation formulas established in strong topology of functional space generated by HSlder norm, we discuss the functional sample path properties of subsequence＇s C-R increments for a Wiener process in HSlder norm. The obtained results, generalize the corresponding results of Chen and the classic Strassen＇s law of iterated logarithm for a Wiener process.展开更多
In this paper, how big the increments are and some liminf behaviors are studied of a two-parameter fractional Wiener process. The results are based on some inequalities on the suprema of this process, which also are o...In this paper, how big the increments are and some liminf behaviors are studied of a two-parameter fractional Wiener process. The results are based on some inequalities on the suprema of this process, which also are of independent interest.展开更多
Let {X(t), t greater than or equal to 0} be a fractional Brownian motion of order 2 alpha with 0 < alpha < 1,beta > 0 be a real number, alpha(T) be a function of T and 0 < alpha(T), [GRAPHICS] (log T/alpha...Let {X(t), t greater than or equal to 0} be a fractional Brownian motion of order 2 alpha with 0 < alpha < 1,beta > 0 be a real number, alpha(T) be a function of T and 0 < alpha(T), [GRAPHICS] (log T/alpha(T))/log T = r, (0 less than or equal to r less than or equal to infinity). In this paper, we proved that [GRAPHICS] where c(1), c(2) are two positive constants depending only on alpha,beta.展开更多
In this paper, based on accurately large deviation formulae established in strong topology generated by the Holder norm for l^2-valued Wiener processes, we obtain the functional limit theorems for C-R increments of l^...In this paper, based on accurately large deviation formulae established in strong topology generated by the Holder norm for l^2-valued Wiener processes, we obtain the functional limit theorems for C-R increments of l^p-valued Wiener processes in the Holder norm.展开更多
Let L(T) be the local time of a Wiener process W(T) for 0 < T < co, and K(w) be the set of limit points (as T → ∞) of L(bk ω) - L(ck, ω)((bk - ok)(log(bk (bk - ck)-1) + 2 log log bk))where ω is a point in t...Let L(T) be the local time of a Wiener process W(T) for 0 < T < co, and K(w) be the set of limit points (as T → ∞) of L(bk ω) - L(ck, ω)((bk - ok)(log(bk (bk - ck)-1) + 2 log log bk))where ω is a point in the probability space on which W(T) is defined. In this paper, under some conditions we obtain P(K(ω) = [0, 1]) = 1.展开更多
The general form of increments of local time L(t) and sup (L(t+s)-L(t)) of a Wiener process has been considered and the condition "non-decreasing’~ assumed by Csáki Csrg, Fldes and Revesz has been removed. ...The general form of increments of local time L(t) and sup (L(t+s)-L(t)) of a Wiener process has been considered and the condition "non-decreasing’~ assumed by Csáki Csrg, Fldes and Revesz has been removed. A theorem has been obtained from the results of Csákl et al.展开更多
Let {W(t): t≥0} be a standard Wiener process and S be the Strassen set of functions. We investigate the exact rates of convergence to zero (as T→∞) of the variables sup_(0≤≤T-a_T inf_(f∈S sup_(0≤r≤1 |Y_t, T(x)...Let {W(t): t≥0} be a standard Wiener process and S be the Strassen set of functions. We investigate the exact rates of convergence to zero (as T→∞) of the variables sup_(0≤≤T-a_T inf_(f∈S sup_(0≤r≤1 |Y_t, T(x)-f(x)] and inf_(0≤t≤T-a_T sup_(0≤x≤1|Y_(t.T)(x)-f(x)| for any given f∈S, where Y_(t.T)(x)=(W(t+xa_T)-W(t))(2a_T(logTa_T^(-1)+log logT))^(-1/2). We establish a relation between how small the increments are and the functional limit results of Csrg-Revesz increments for a Wiener process. Similar results for partial sums of i.i.d, random variables are also given.展开更多
Abstract In this paper, a liminf behavior is studied of a two-parameter Gaussian process which is a generalization of a two-parameter Wiener process. The results improve on the liminfs in [7].
基金Supported by the National Natural Science Foundation of ChinaZhejiang Province Natural Science Fund
文摘In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of increments. Our results imply the theorem that have been given by Csorgo and Revesz (1978), and some of their conditions are removed.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10131040)China Postdoctoral Science Foundation.
文摘In this paper, we prove a theorem on the set of limit points of the increments of a two-parameter Wiener process via establishing a large deviation principle on the increments of the two-parameter Wiener process.
文摘A general form of the increments of two-parameter fractional Wiener process is given. The results of Csoergo-Révész increments are a special case,and it also implies the results of the increments of the two-parameter Wiener process.
基金Supported by the Natural Science Foundation of Hubei Province of China(2011CDB229)
文摘In this paper, with the aid of large deviation formulas established in strong topology of functional space generated by HSlder norm, we discuss the functional sample path properties of subsequence＇s C-R increments for a Wiener process in HSlder norm. The obtained results, generalize the corresponding results of Chen and the classic Strassen＇s law of iterated logarithm for a Wiener process.
基金the National Natural Science Foundation of China (Grant No. 10071072) by NSC 88-2118-M029-001 of Taiwan of China.
文摘In this paper, how big the increments are and some liminf behaviors are studied of a two-parameter fractional Wiener process. The results are based on some inequalities on the suprema of this process, which also are of independent interest.
文摘Let {X(t), t greater than or equal to 0} be a fractional Brownian motion of order 2 alpha with 0 < alpha < 1,beta > 0 be a real number, alpha(T) be a function of T and 0 < alpha(T), [GRAPHICS] (log T/alpha(T))/log T = r, (0 less than or equal to r less than or equal to infinity). In this paper, we proved that [GRAPHICS] where c(1), c(2) are two positive constants depending only on alpha,beta.
文摘In this paper, based on accurately large deviation formulae established in strong topology generated by the Holder norm for l^2-valued Wiener processes, we obtain the functional limit theorems for C-R increments of l^p-valued Wiener processes in the Holder norm.
文摘Let L(T) be the local time of a Wiener process W(T) for 0 < T < co, and K(w) be the set of limit points (as T → ∞) of L(bk ω) - L(ck, ω)((bk - ok)(log(bk (bk - ck)-1) + 2 log log bk))where ω is a point in the probability space on which W(T) is defined. In this paper, under some conditions we obtain P(K(ω) = [0, 1]) = 1.
基金Project supported by the National Natural Science Foundation of China and Fok Ying Tong Education Foundations.
文摘The general form of increments of local time L(t) and sup (L(t+s)-L(t)) of a Wiener process has been considered and the condition "non-decreasing’~ assumed by Csáki Csrg, Fldes and Revesz has been removed. A theorem has been obtained from the results of Csákl et al.
基金Project supported by National Science Foundation of ChinaZhejiang Province
文摘Let {W(t): t≥0} be a standard Wiener process and S be the Strassen set of functions. We investigate the exact rates of convergence to zero (as T→∞) of the variables sup_(0≤≤T-a_T inf_(f∈S sup_(0≤r≤1 |Y_t, T(x)-f(x)] and inf_(0≤t≤T-a_T sup_(0≤x≤1|Y_(t.T)(x)-f(x)| for any given f∈S, where Y_(t.T)(x)=(W(t+xa_T)-W(t))(2a_T(logTa_T^(-1)+log logT))^(-1/2). We establish a relation between how small the increments are and the functional limit results of Csrg-Revesz increments for a Wiener process. Similar results for partial sums of i.i.d, random variables are also given.
基金Supported by the National Natural Science Foundation of China (No.10071072).
文摘Abstract In this paper, a liminf behavior is studied of a two-parameter Gaussian process which is a generalization of a two-parameter Wiener process. The results improve on the liminfs in [7].
