Suppose that X is a right process which is associated with a semi-Dirichlet form （ε, D（ε）） on L2（E; m）. Let J be the jumping measure of （ε, D（ε）） satisfying J（E x E- d） 〈 ∞. Let u E D（ε）b ：= D（...Suppose that X is a right process which is associated with a semi-Dirichlet form （ε, D（ε）） on L2（E; m）. Let J be the jumping measure of （ε, D（ε）） satisfying J（E x E- d） 〈 ∞. Let u E D（ε）b ：= D（ε） N L（E; m）, we have the following Pukushima＇s decomposition u（Xt）-u（X0） --- Mut ＋ Nut. Define Pu f（x） = Ex[eNT f（Xt）]. Let Qu（f,g） = ε（f,g）＋ε（u, fg） for f, g E D（ε）b. In the first part, under some assumptions we show that （Qu, D（ε）b） is lower semi-bounded if and only if there exists a constant a0 〉 0 such that /Put/2 ≤eaot for every t 〉 0. If one of these assertions holds, then （Put〉0is strongly continuous on L2（E;m）. If X is equipped with a differential structure, then under some other assumptions, these conclusions remain valid without assuming J（E x E - d） 〈 ∞. Some examples are also given in this part. Let At be a local continuous additive functional with zero quadratic variation. In the second part, we get the representation of At and give two sufficient conditions for PAf（x） = Ex[eAtf（Xt）] to be strongly continuous.展开更多
Let u={u(t,x),t∈[0,T],x∈R}be a solution to a stochastic heat equation driven by a space-time white noise.We study that the realized power variation of the process u with respect to the time,properly normalized,has G...Let u={u(t,x),t∈[0,T],x∈R}be a solution to a stochastic heat equation driven by a space-time white noise.We study that the realized power variation of the process u with respect to the time,properly normalized,has Gaussian asymptotic distributions.In particular,we study the realized power variation of the process u with respect to the time converges weakly to Brownian motion.展开更多
In this paper we study tree martingales and proved that if 1≤α,β〈∞,1≤p〈∞ then for every predictable tree martingale f=（ft,t∞T）and E[σ^（P）（f）]〈∞,E[S^（P）（f）]〈∞,it holds that ‖（St^（p）（f）,t∈...In this paper we study tree martingales and proved that if 1≤α,β〈∞,1≤p〈∞ then for every predictable tree martingale f=（ft,t∞T）and E[σ^（P）（f）]〈∞,E[S^（P）（f）]〈∞,it holds that ‖（St^（p）（f）,t∈T）‖M^α∞≤Cαβ‖f‖p^αβ,‖（σt^（p）（f）,t∈T）‖M^α,β‖f‖P^αβ,where Cαβ depends only on α and β.展开更多
This study examines the use of high frequency data in finance,including volatility estimation and jump tests.High frequency data allows the construction of model-free volatility measures for asset returns.Realized var...This study examines the use of high frequency data in finance,including volatility estimation and jump tests.High frequency data allows the construction of model-free volatility measures for asset returns.Realized variance is a consistent estimator of quadratic variation under mild regularity conditions.Other variation concepts,such as power variation and bipower variation,are useful and important for analyzing high frequency data when jumps are present.High frequency data can also be used to test jumps in asset prices.We discuss three jump tests:bipower variation test,power variation test,and variance swap test in this study.The presence of market microstructure noise complicates the analysis of high frequency data.The survey introduces several robust methods of volatility estimation and jump tests in the presence of market microstructure noise.Finally,some applications of jump tests in asset pricing are discussed in this article.展开更多
基金supported by NSFC(11201102,11326169,11361021)Natural Science Foundation of Hainan Province(112002,113007)
文摘Suppose that X is a right process which is associated with a semi-Dirichlet form （ε, D（ε）） on L2（E; m）. Let J be the jumping measure of （ε, D（ε）） satisfying J（E x E- d） 〈 ∞. Let u E D（ε）b ：= D（ε） N L（E; m）, we have the following Pukushima＇s decomposition u（Xt）-u（X0） --- Mut ＋ Nut. Define Pu f（x） = Ex[eNT f（Xt）]. Let Qu（f,g） = ε（f,g）＋ε（u, fg） for f, g E D（ε）b. In the first part, under some assumptions we show that （Qu, D（ε）b） is lower semi-bounded if and only if there exists a constant a0 〉 0 such that /Put/2 ≤eaot for every t 〉 0. If one of these assertions holds, then （Put〉0is strongly continuous on L2（E;m）. If X is equipped with a differential structure, then under some other assumptions, these conclusions remain valid without assuming J（E x E - d） 〈 ∞. Some examples are also given in this part. Let At be a local continuous additive functional with zero quadratic variation. In the second part, we get the representation of At and give two sufficient conditions for PAf（x） = Ex[eAtf（Xt）] to be strongly continuous.
基金Supported by ZJNSF(Grant No.LY20A010020)NSFC(Grant No.11671115)。
文摘Let u={u(t,x),t∈[0,T],x∈R}be a solution to a stochastic heat equation driven by a space-time white noise.We study that the realized power variation of the process u with respect to the time,properly normalized,has Gaussian asymptotic distributions.In particular,we study the realized power variation of the process u with respect to the time converges weakly to Brownian motion.
基金Supported by The National Natural Science Foundation of China （No.10371093）Acknowledgements. The authors would like to thank Professor Pei-De Liu for his valuable suggestions and express their gratitude to the referee for his very helpful and detailed comments.
文摘In this paper we study tree martingales and proved that if 1≤α,β〈∞,1≤p〈∞ then for every predictable tree martingale f=（ft,t∞T）and E[σ^（P）（f）]〈∞,E[S^（P）（f）]〈∞,it holds that ‖（St^（p）（f）,t∈T）‖M^α∞≤Cαβ‖f‖p^αβ,‖（σt^（p）（f）,t∈T）‖M^α,β‖f‖P^αβ,where Cαβ depends only on α and β.
文摘This study examines the use of high frequency data in finance,including volatility estimation and jump tests.High frequency data allows the construction of model-free volatility measures for asset returns.Realized variance is a consistent estimator of quadratic variation under mild regularity conditions.Other variation concepts,such as power variation and bipower variation,are useful and important for analyzing high frequency data when jumps are present.High frequency data can also be used to test jumps in asset prices.We discuss three jump tests:bipower variation test,power variation test,and variance swap test in this study.The presence of market microstructure noise complicates the analysis of high frequency data.The survey introduces several robust methods of volatility estimation and jump tests in the presence of market microstructure noise.Finally,some applications of jump tests in asset pricing are discussed in this article.
