In this paper we study p-variation of bifractional Brownian motion. As an applica-tion, we introduce a class of estimators of the parameters of a bifractional Brownian motion andprove that both of them are strongly co...In this paper we study p-variation of bifractional Brownian motion. As an applica-tion, we introduce a class of estimators of the parameters of a bifractional Brownian motion andprove that both of them are strongly consistent; as another application, we investigate fractalnature related to the box dimension of the graph of bifractional Brownian motion.展开更多
Let B^H＇K={B^H＇K（t）, t∈R＋^N} be an （N,d）-bifractional Brownian sheet with Hurst indices H = （H1,…,HN） C∈0,1）^N and K = （K1,…,KN） ∈ （0,1]^N. The properties of the polar sets of B^H＇K are discussed. T...Let B^H＇K={B^H＇K（t）, t∈R＋^N} be an （N,d）-bifractional Brownian sheet with Hurst indices H = （H1,…,HN） C∈0,1）^N and K = （K1,…,KN） ∈ （0,1]^N. The properties of the polar sets of B^H＇K are discussed. The sufficient conditions and necessary conditions for a compact set to be polar for B^H＇K are proved. The infimum of Hausdorff dimensions of its non-polar sets are obtained by means of constructing a Cantor-type set to connect its Hausdorff dimension and capacity.展开更多
In this paper, we consider the local time and the self-intersection local time for a bifractional Brownian motion, and the collision local time for two independent bifractional Brownian motions. We mainly prove the ex...In this paper, we consider the local time and the self-intersection local time for a bifractional Brownian motion, and the collision local time for two independent bifractional Brownian motions. We mainly prove the existence and smoothness of the self-intersection local time and the collision local time, through the strong local nondeterminism of bifractional Brownian motion, L2 convergence and Chaos expansion.展开更多
Let B^Hi,Ki={Bt^Hi,Ki,t≥0},i=1,2 be two independent bifractional Brownian motions with respective indices Hi∈(0,1)and K∈E(0,1].One of the main motivations of this paper is to investigate f0^Tδ(Bs^H1,K1-the smoothn...Let B^Hi,Ki={Bt^Hi,Ki,t≥0},i=1,2 be two independent bifractional Brownian motions with respective indices Hi∈(0,1)and K∈E(0,1].One of the main motivations of this paper is to investigate f0^Tδ(Bs^H1,K1-the smoothness of the collision local time,introduced by Jiang and Wang in 2009,IT=f0^Tδ(Bs^H1,K1)ds,T〉0,where 6 denotes the Dirac delta function.By an elementary method,we show that iT is smooth in the sense of the Meyer-Watanabe if and only if min{H-1K1,H2K2}〈-1/3.展开更多
Let BH,K={BH,K(t),t∈R+}be a bifractional Brownian motion in Rd.This process is a selfsimilar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of fractional Brownian mot...Let BH,K={BH,K(t),t∈R+}be a bifractional Brownian motion in Rd.This process is a selfsimilar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of fractional Brownian motion(which is obtained for K=1).The exact Hausdorff measures of the image,graph and the level set of BH,K are investigated.The results extend the corresponding results proved by Talagrand and Xiao for fractional Brownian motion.展开更多
Let B^H,K ： （B^H,K（t）, t ∈R＋^N} be an （N,d）-bifractional Brownian sheet with Hurst indices H = （H1,..., HN） ∈ （0, 1）^N and K = （K1,..., KN）∈ （0, 1]^N. The characteristics of the polar functions for B^...Let B^H,K ： （B^H,K（t）, t ∈R＋^N} be an （N,d）-bifractional Brownian sheet with Hurst indices H = （H1,..., HN） ∈ （0, 1）^N and K = （K1,..., KN）∈ （0, 1]^N. The characteristics of the polar functions for B^H,K are investigated. The relationship between the class of continuous functions satisfying the Lipschitz condition and the class of polar-functions of B^H,K is presented. The Hausdorff dimension of the fixed points and an inequality concerning the Kolmogorov＇s entropy index for B^H,K are obtained. A question proposed by LeGall about the existence of no-polar, continuous functions statisfying the Holder condition is also solved.展开更多
We show in this work that the limit in law of the cross-variation of processes having the form of Young integral with respect to a general self-similar centered Gaussian process of orderβ∈(1/2,3/4]is normal accordin...We show in this work that the limit in law of the cross-variation of processes having the form of Young integral with respect to a general self-similar centered Gaussian process of orderβ∈(1/2,3/4]is normal according to the values ofβ.We apply our results to two self-similar Gaussian processes:the subfractional Brownian motion and the bifractional Brownian motion.展开更多
European compound option pricing model is established by using the mixed bifractional Brownian motion. Firstly, using the principle of risk-neutral pricing, the European option pricing formulas and the parity formulas...European compound option pricing model is established by using the mixed bifractional Brownian motion. Firstly, using the principle of risk-neutral pricing, the European option pricing formulas and the parity formulas are obtained. Secondly, with the Delta hedging strategy, the corresponding compound option pricing formulas and the parity formulas are got. Finally, using the daily closing price data of “Lingang B shares” and “Yitai B shares” respectively, the results show that the mixed model is closer to the true value than the previous model.展开更多
基金supported by NSFC (11071076)NSFC-NSF (10911120392)
文摘In this paper we study p-variation of bifractional Brownian motion. As an applica-tion, we introduce a class of estimators of the parameters of a bifractional Brownian motion andprove that both of them are strongly consistent; as another application, we investigate fractalnature related to the box dimension of the graph of bifractional Brownian motion.
基金supported by the national natural foundationof China (70871104)the key research base for humanities and social sciences of Zhejiang Provincial high education talents (Statistics of Zhejiang Gongshang University)
文摘Let B^H＇K={B^H＇K（t）, t∈R＋^N} be an （N,d）-bifractional Brownian sheet with Hurst indices H = （H1,…,HN） C∈0,1）^N and K = （K1,…,KN） ∈ （0,1]^N. The properties of the polar sets of B^H＇K are discussed. The sufficient conditions and necessary conditions for a compact set to be polar for B^H＇K are proved. The infimum of Hausdorff dimensions of its non-polar sets are obtained by means of constructing a Cantor-type set to connect its Hausdorff dimension and capacity.
基金supported by National Natural Science Foundation of China (Grant No.10871103)
文摘In this paper, we consider the local time and the self-intersection local time for a bifractional Brownian motion, and the collision local time for two independent bifractional Brownian motions. We mainly prove the existence and smoothness of the self-intersection local time and the collision local time, through the strong local nondeterminism of bifractional Brownian motion, L2 convergence and Chaos expansion.
基金supported by National Natural Science Foundation of China(Grant No.10871041)Key Natural Science Foundation of Anhui Educational Committee(Grant No.KJ2011A139)
文摘Let B^Hi,Ki={Bt^Hi,Ki,t≥0},i=1,2 be two independent bifractional Brownian motions with respective indices Hi∈(0,1)and K∈E(0,1].One of the main motivations of this paper is to investigate f0^Tδ(Bs^H1,K1-the smoothness of the collision local time,introduced by Jiang and Wang in 2009,IT=f0^Tδ(Bs^H1,K1)ds,T〉0,where 6 denotes the Dirac delta function.By an elementary method,we show that iT is smooth in the sense of the Meyer-Watanabe if and only if min{H-1K1,H2K2}〈-1/3.
基金supported by National Natural Science Foundation of China(Grant No.10721091)
文摘Let BH,K={BH,K(t),t∈R+}be a bifractional Brownian motion in Rd.This process is a selfsimilar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of fractional Brownian motion(which is obtained for K=1).The exact Hausdorff measures of the image,graph and the level set of BH,K are investigated.The results extend the corresponding results proved by Talagrand and Xiao for fractional Brownian motion.
基金Supported by the National Natural Science Foundation of China(No.70471071)the Key Research Base for Humanities and Social Sciences of Zhejiang Provincial High Education Talents(Statistics of Zhejiang Gongshang University).
文摘Let B^H,K ： （B^H,K（t）, t ∈R＋^N} be an （N,d）-bifractional Brownian sheet with Hurst indices H = （H1,..., HN） ∈ （0, 1）^N and K = （K1,..., KN）∈ （0, 1]^N. The characteristics of the polar functions for B^H,K are investigated. The relationship between the class of continuous functions satisfying the Lipschitz condition and the class of polar-functions of B^H,K is presented. The Hausdorff dimension of the fixed points and an inequality concerning the Kolmogorov＇s entropy index for B^H,K are obtained. A question proposed by LeGall about the existence of no-polar, continuous functions statisfying the Holder condition is also solved.
基金The first author was supported by the Fulbright joint supervision program for PhD students for the academic year 2018-2019 between Cadi Ayyad University and Michigan State University.
文摘We show in this work that the limit in law of the cross-variation of processes having the form of Young integral with respect to a general self-similar centered Gaussian process of orderβ∈(1/2,3/4]is normal according to the values ofβ.We apply our results to two self-similar Gaussian processes:the subfractional Brownian motion and the bifractional Brownian motion.
文摘European compound option pricing model is established by using the mixed bifractional Brownian motion. Firstly, using the principle of risk-neutral pricing, the European option pricing formulas and the parity formulas are obtained. Secondly, with the Delta hedging strategy, the corresponding compound option pricing formulas and the parity formulas are got. Finally, using the daily closing price data of “Lingang B shares” and “Yitai B shares” respectively, the results show that the mixed model is closer to the true value than the previous model.
