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
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
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
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.
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.
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.
