This paper considers a nonparametric M-estimator of a regression function for functional stationary ergodic data.More precisely,in the ergodic data setting,we consider the regression of a real random variable Y over a...This paper considers a nonparametric M-estimator of a regression function for functional stationary ergodic data.More precisely,in the ergodic data setting,we consider the regression of a real random variable Y over an explanatory random variable X taking values in some semi-metric abstract space.Under some mild conditions,the weak consistency and the asymptotic normality of the M-estimator are established.Furthermore,a simulated example is provided to examine the finite sample performance of the M-estimator.展开更多
Let {W(t),t∈R}, {B(t),t∈R+} be two independent Brownian motions on R with W(0) = B(0) = 0. In this paper, we shall consider the exact Hausdorff measures for the image and graph sets of the d-dimensional iterated Bro...Let {W(t),t∈R}, {B(t),t∈R+} be two independent Brownian motions on R with W(0) = B(0) = 0. In this paper, we shall consider the exact Hausdorff measures for the image and graph sets of the d-dimensional iterated Brownian motion X(t), where X(t) = (Xi(t),... ,Xd(t)) and X1(t),... ,Xd(t) are d independent copies of Y(t) = W(B(t)). In particular, for any Borel set Q (?) (0,∞), the exact Hausdorff measures of the image X(Q) = {X(t) : t∈Q} and the graph GrX(Q) = {(t, X(t)) :t∈Q}are established.展开更多
Let{W1(t), t∈R+} and {W2(t), t∈R+} be two independent Brownian motions with W1(0) = W2(0) = 0. {H (t) = W1(|W2(t)|), t ∈R+} is called a generalized iterated Brownian motion. In this paper, the Ha...Let{W1(t), t∈R+} and {W2(t), t∈R+} be two independent Brownian motions with W1(0) = W2(0) = 0. {H (t) = W1(|W2(t)|), t ∈R+} is called a generalized iterated Brownian motion. In this paper, the Hausdorff dimension and packing dimension of the level sets {t ∈[0, T ], H(t) = x} are established for any 0 T ≤ 1.展开更多
Let B0^H = {B0^H(t),t ∈ R+^N) be a real-valued fractional Brownian sheet. Define the (N,d)- Gaussian random field B^H by B^H(t) = (B1^H(t),...,Bd^H(t)) t ∈ R+^N, where B1^H, ..., Bd^H are independent...Let B0^H = {B0^H(t),t ∈ R+^N) be a real-valued fractional Brownian sheet. Define the (N,d)- Gaussian random field B^H by B^H(t) = (B1^H(t),...,Bd^H(t)) t ∈ R+^N, where B1^H, ..., Bd^H are independent copies of B0^H. The existence and joint continuity of local times of B^H is proven in some given conditions in [22]. We then study further properties of the local times of B^H, such as the moments of increments of local times, the large increments and the maximum moduli of continuity of local times and as a result, we answer the questions posed in [22].展开更多
In this paper, we introduce a class of Gaussian processes Y={Y(t):t∈R^N},the so called hifractional Brownian motion with the indcxes H=(H1,…,HN)and α. We consider the (N, d, H, α) Gaussian random field x(t...In this paper, we introduce a class of Gaussian processes Y={Y(t):t∈R^N},the so called hifractional Brownian motion with the indcxes H=(H1,…,HN)and α. We consider the (N, d, H, α) Gaussian random field x(t) = (x1 (t),..., xd(t)),where X1 (t),…, Xd(t) are independent copies of Y(t), At first we show the existence and join continuity of the local times of X = {X(t), t ∈ R+^N}, then we consider the HSlder conditions for the local times.展开更多
基金supported by National Natural Science Foundation of China(No.11301084)Natural Science Foundation of Fujian Province,China(No.2014J01010)
文摘This paper considers a nonparametric M-estimator of a regression function for functional stationary ergodic data.More precisely,in the ergodic data setting,we consider the regression of a real random variable Y over an explanatory random variable X taking values in some semi-metric abstract space.Under some mild conditions,the weak consistency and the asymptotic normality of the M-estimator are established.Furthermore,a simulated example is provided to examine the finite sample performance of the M-estimator.
基金This work was partially supported by the National Natural Science Foundation of China (Grant No. 10131040)China Postdoctoral Science Foundation.
文摘Let {W(t),t∈R}, {B(t),t∈R+} be two independent Brownian motions on R with W(0) = B(0) = 0. In this paper, we shall consider the exact Hausdorff measures for the image and graph sets of the d-dimensional iterated Brownian motion X(t), where X(t) = (Xi(t),... ,Xd(t)) and X1(t),... ,Xd(t) are d independent copies of Y(t) = W(B(t)). In particular, for any Borel set Q (?) (0,∞), the exact Hausdorff measures of the image X(Q) = {X(t) : t∈Q} and the graph GrX(Q) = {(t, X(t)) :t∈Q}are established.
基金Supported by the National Science Foundation of Zhejiang(No.LQ12F03003)
文摘Let{W1(t), t∈R+} and {W2(t), t∈R+} be two independent Brownian motions with W1(0) = W2(0) = 0. {H (t) = W1(|W2(t)|), t ∈R+} is called a generalized iterated Brownian motion. In this paper, the Hausdorff dimension and packing dimension of the level sets {t ∈[0, T ], H(t) = x} are established for any 0 T ≤ 1.
基金Supported by the National Natural Science Foundation of China(No.10571159)Specialized Research Found for Doctor Program of Higher Education(No.20060335032)Hangdian Foundation(No.KYS091506042).
文摘Let B0^H = {B0^H(t),t ∈ R+^N) be a real-valued fractional Brownian sheet. Define the (N,d)- Gaussian random field B^H by B^H(t) = (B1^H(t),...,Bd^H(t)) t ∈ R+^N, where B1^H, ..., Bd^H are independent copies of B0^H. The existence and joint continuity of local times of B^H is proven in some given conditions in [22]. We then study further properties of the local times of B^H, such as the moments of increments of local times, the large increments and the maximum moduli of continuity of local times and as a result, we answer the questions posed in [22].
基金Supported by the National Natural Science Foundation of China(No.10571159)Specialized Research Fund for the Doctor Program of Higher Education(No.2002335090)
文摘In this paper, we introduce a class of Gaussian processes Y={Y(t):t∈R^N},the so called hifractional Brownian motion with the indcxes H=(H1,…,HN)and α. We consider the (N, d, H, α) Gaussian random field x(t) = (x1 (t),..., xd(t)),where X1 (t),…, Xd(t) are independent copies of Y(t), At first we show the existence and join continuity of the local times of X = {X(t), t ∈ R+^N}, then we consider the HSlder conditions for the local times.