Let S = {（St1,···,Std ）}t≥0 denote a d-dimensional sub-fractional Brownian motion with index H ≥ 1/2. In this paper we study some properties of the process X of the formwhere Rt = （（St1）2＋·...Let S = {（St1,···,Std ）}t≥0 denote a d-dimensional sub-fractional Brownian motion with index H ≥ 1/2. In this paper we study some properties of the process X of the formwhere Rt = （（St1）2＋···＋（Std）2）~1/2 is the sub-fractional Bessel process.展开更多
In this paper,wewill first give the numerical simulation of the sub-fractional Brownian motion through the relation of fractional Brownian motion instead of its representation of random walk.In order to verify the rat...In this paper,wewill first give the numerical simulation of the sub-fractional Brownian motion through the relation of fractional Brownian motion instead of its representation of random walk.In order to verify the rationality of this simulation,we propose a practical estimator associated with the LSE of the drift parameter of mixed sub-fractional Ornstein-Uhlenbeck process,and illustrate the asymptotical properties according to our method of simulation when the Hurst parameter H>1/2.展开更多
Let SH be a sub-fractional Brownian motion with index 0 < H < 1/2.In this paper we study the existence of the generalized quadratic covariation [f(SH),SH](W) defned by[f(SH), SH](W)t= limε→01/ε2H∫t0{f(SHs+ε...Let SH be a sub-fractional Brownian motion with index 0 < H < 1/2.In this paper we study the existence of the generalized quadratic covariation [f(SH),SH](W) defned by[f(SH), SH](W)t= limε→01/ε2H∫t0{f(SHs+ε)-f(SHs)}(SHs+ε-SHs)ds2H,provided the limit exists in probability, where x → f(x) is a measurable function. We construct a Banach space ■ of measurable functions such that the generalized quadratic covariation exists in L2 provided f ∈ H.Moreover, the generalized Bouleau-Yor identity takes the form ∫Rf(x)ψH(dx, t) =(2-22H-1)[f(SH), SH](W)t for all f∈■, where ψH(x, t) is the weighted local time of SH. This allows us to write the generalized It's formula for absolutely continuous functions with derivative belonging to展开更多
以塔里木3种稠油为原料，对稠油进行四组分的分离，测定了稠油及各组分的C、H、S、N及金属镍、钒、钙、铜、铁、钾、钠和铅的含量，研究了各金属在稠油组分中的分布，并进行了红外光谱分析。结果表明，相同条件下，3种稠油及其四组分在C...以塔里木3种稠油为原料，对稠油进行四组分的分离，测定了稠油及各组分的C、H、S、N及金属镍、钒、钙、铜、铁、钾、钠和铅的含量，研究了各金属在稠油组分中的分布，并进行了红外光谱分析。结果表明，相同条件下，3种稠油及其四组分在C、H元素的含量上差别不大，N元素富集在胶质和沥青质中，S元素主要存在于芳香分、胶质及沥青质中，3种稠油的饱和分中均含有微量的N、S元素。在3种稠油中，各金属元素在饱和分和芳香分中含量很低，随着组分的变重，含量急剧增加。3种稠油中的金属元素主要富集在沥青质中，其次是在胶质中。3种稠油饱和分的官能团种类几乎无差别，稠油的饱和分红外谱图在2800～3100 cm -1和1350～1390 cm -1出现甲基和亚甲基的强吸收峰。展开更多
Let {S t H, t ≥ 0） be a linear combination of a Brownian motion and an independent sub-fractional Brownian motion with Hurst index 0 〈 H 〈 1. Its main properties are studied. They suggest that SH lies between the ...Let {S t H, t ≥ 0） be a linear combination of a Brownian motion and an independent sub-fractional Brownian motion with Hurst index 0 〈 H 〈 1. Its main properties are studied. They suggest that SH lies between the sub-fractional Brownian motion and the mixed fractional Brownian motion. We also determine the values of H for which SH is not a semi-martingale.展开更多
基金Supported by the NSFC (10871041)Key NSF of Anhui Educational Committe (KJ2011A139)
文摘Let S = {（St1,···,Std ）}t≥0 denote a d-dimensional sub-fractional Brownian motion with index H ≥ 1/2. In this paper we study some properties of the process X of the formwhere Rt = （（St1）2＋···＋（Std）2）~1/2 is the sub-fractional Bessel process.
基金supported by the Fundamental Research Funds for the SUFE No.2020110294supported by the National Natural Science Foundation of China,Grant No.71871202.
文摘In this paper,wewill first give the numerical simulation of the sub-fractional Brownian motion through the relation of fractional Brownian motion instead of its representation of random walk.In order to verify the rationality of this simulation,we propose a practical estimator associated with the LSE of the drift parameter of mixed sub-fractional Ornstein-Uhlenbeck process,and illustrate the asymptotical properties according to our method of simulation when the Hurst parameter H>1/2.
基金supported by National Natural Science Foundation of China(Grant No.11171062)Innovation Program of Shanghai Municipal Education Commission(Grant No.12ZZ063)
文摘Let SH be a sub-fractional Brownian motion with index 0 < H < 1/2.In this paper we study the existence of the generalized quadratic covariation [f(SH),SH](W) defned by[f(SH), SH](W)t= limε→01/ε2H∫t0{f(SHs+ε)-f(SHs)}(SHs+ε-SHs)ds2H,provided the limit exists in probability, where x → f(x) is a measurable function. We construct a Banach space ■ of measurable functions such that the generalized quadratic covariation exists in L2 provided f ∈ H.Moreover, the generalized Bouleau-Yor identity takes the form ∫Rf(x)ψH(dx, t) =(2-22H-1)[f(SH), SH](W)t for all f∈■, where ψH(x, t) is the weighted local time of SH. This allows us to write the generalized It's formula for absolutely continuous functions with derivative belonging to
文摘以塔里木3种稠油为原料，对稠油进行四组分的分离，测定了稠油及各组分的C、H、S、N及金属镍、钒、钙、铜、铁、钾、钠和铅的含量，研究了各金属在稠油组分中的分布，并进行了红外光谱分析。结果表明，相同条件下，3种稠油及其四组分在C、H元素的含量上差别不大，N元素富集在胶质和沥青质中，S元素主要存在于芳香分、胶质及沥青质中，3种稠油的饱和分中均含有微量的N、S元素。在3种稠油中，各金属元素在饱和分和芳香分中含量很低，随着组分的变重，含量急剧增加。3种稠油中的金属元素主要富集在沥青质中，其次是在胶质中。3种稠油饱和分的官能团种类几乎无差别，稠油的饱和分红外谱图在2800～3100 cm -1和1350～1390 cm -1出现甲基和亚甲基的强吸收峰。
文摘Let {S t H, t ≥ 0） be a linear combination of a Brownian motion and an independent sub-fractional Brownian motion with Hurst index 0 〈 H 〈 1. Its main properties are studied. They suggest that SH lies between the sub-fractional Brownian motion and the mixed fractional Brownian motion. We also determine the values of H for which SH is not a semi-martingale.
