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
Let W={W(t);t ∈R_+~N} be the d-dimensional N-parameter Brownian Sheet. Sufficient conditions for a compact set F C Rd \ {0} to be a polar set for W are proved. It is also proved that if 2N≤d, then for any compact se...Let W={W(t);t ∈R_+~N} be the d-dimensional N-parameter Brownian Sheet. Sufficient conditions for a compact set F C Rd \ {0} to be a polar set for W are proved. It is also proved that if 2N≤d, then for any compact set E (?)R_>~N ,inf {dimF : F ∈B(Rd), P{W(E) ∩F≠(?)}>0} = d- 2DiroE, and if 2N > d, then for any compact set F C Rd \ {0}, inf{dim E : E ∈ B(R_>~N), P{W(E)∩F≠(?)}>0}=d/2-DimF/2,where B(Rd) and B(R_>~N) denote the Borel σ-algebra in Rd and R_>~N respectively, and dim and Dim are Hausdorff dimension and Packing dimension respectively.展开更多
This paper studies fractal properties of polar sets for random string processes. We give upper and lower bounds of the hitting probabilities on compact sets and prove some sufficient conditions and necessary condition...This paper studies fractal properties of polar sets for random string processes. We give upper and lower bounds of the hitting probabilities on compact sets and prove some sufficient conditions and necessary conditions for compact sets to be polar for the random string process. Moreover, we also determine the smallest Hausdorff dimensions of non-polar sets by constructing a Cantor-type set to connect its Hausdorff dimension and capacity.展开更多
Let W^-（t）（t∈R＋^N） be the d-dimensional N-parameter generalized Brownian sheet. We study the polar sets for W^-（t）. It is proved that for any α∈ R^d, P{W^-（t） = α, for some t∈ R〉^N} = {1, if βd 〈 2N ...Let W^-（t）（t∈R＋^N） be the d-dimensional N-parameter generalized Brownian sheet. We study the polar sets for W^-（t）. It is proved that for any α∈ R^d, P{W^-（t） = α, for some t∈ R〉^N} = {1, if βd 〈 2N ,0 if αd〉 2N and the probability that W^-（t） has k-multiple points is 1 or 0 according as whether 2kN〉d（k-1）β or 2kN 〈 d（k - 1）α. These results contain and extend the results of the Brownian sheet, where R〉^N = （0,＋∞）U,R＋^N = [0,＋∞）^N,0〈 α ≤1and β〉1.展开更多
Let W^～=^～{W^～（t）; t∈ R＋^N） be a d-dimensional N-parameter generalized Brownian sheet. Necessary and sufficient conditions for a compact set E × F to be a polar set for （t,W^～（t）） are proved. It is a...Let W^～=^～{W^～（t）; t∈ R＋^N） be a d-dimensional N-parameter generalized Brownian sheet. Necessary and sufficient conditions for a compact set E × F to be a polar set for （t,W^～（t）） are proved. It is also proved that if 2N ≤αd, then for any compact set E ∩→ R〉^N,d-2/α Dim E≤inf{dim F：F∈B（R^d）,P{W^～（E）∩F≠0}〉0}≤d-2/βDimE,and if 2N〉αd, then for any compact set F∪→R^d／{0},α/2（d-DimF）≤inf{dimE：E∈B（R〉^N）,P{W^～（E）∩F≠0}〉0}≤β/2（d-DimF）,where B（R^d） and B（R〉^N） denote the Borel σ-algebra in R^d and in R〉^N respectively, dim and Dim are Hausdorff dimension and Packing dimension respectively.展开更多
This paper gives probabilistic expressions of theminimal and maximal positive solutions of the partial differential equation -1/2△v(x) + γ(x)v(x)α = 0 in D, where D is a regular domain in Rd(d ≥ 3) such that its c...This paper gives probabilistic expressions of theminimal and maximal positive solutions of the partial differential equation -1/2△v(x) + γ(x)v(x)α = 0 in D, where D is a regular domain in Rd(d ≥ 3) such that its complement Dc is compact, γ(x) is a positive bounded integrable function in D, and 1 ＜α≤ 2. As an application, some necessary and sufficient conditions for a compact set to be S-polar are presented.展开更多
The anthem investigate the hitting probability, polarity and the relationship between the polarity and Hausdorff dimension for self-similar Markov processes with state space (0, infinity) and increasing path.
Polar set of Markov processes is an important concept in probabilistic potential theory, but it is not easy to judge the polarity of the sets. In this paper, we give some results which can be easily used to examine th...Polar set of Markov processes is an important concept in probabilistic potential theory, but it is not easy to judge the polarity of the sets. In this paper, we give some results which can be easily used to examine the polarity of the sets whenX t belongs to a special class of Levy processes. We also give a result about polar functions of symmetric stable processes.展开更多
针对极化码在中短码长时纠错性能的不足,提出了一种基于错误集的极化码改进串行抵消列表(Successive Cancellation List of Polar Codes Based on Error Set,ES-SCL)译码算法。该算法首先根据极化码的信道特性构造错误集,在极化码编码...针对极化码在中短码长时纠错性能的不足,提出了一种基于错误集的极化码改进串行抵消列表(Successive Cancellation List of Polar Codes Based on Error Set,ES-SCL)译码算法。该算法首先根据极化码的信道特性构造错误集,在极化码编码时根据错误集中的元素设置奇偶校验(Parity Check,PC)位,其余位置则放置信息比特和冻结比特,译码器在译码PC位时,每条路径通过校验函数得到PC位的比特估计,不执行路径分裂和剪枝,其余位置则执行SCL译码。仿真结果表明,在加性高斯白噪声信道下,当码长为512,码率为0.5,误块率为10^(-5),最大译码列表数为8时,相较于PC-PSCL译码算法以及CA-SCL译码算法,所提出的ES-SCL译码算法获得了约0.18和0.15 dB的增益;当码长为256,码率为0.5,误码率为10^(-5),最大译码列表数为8时,相较于CA-SCL,PC-PSCL译码算法,获得了约0.3和0.35 dB的增益;此外,采用部分比特分裂译码的ES-SCL译码算法可以在误块率与PC-PSCL译码算法几乎相同的情况下,减少约50%的排序次数,具有更低的译码复杂度。展开更多
针对基于路径分裂策略辅助极化码串行抵消列表(Path Splitting Selecting strategy based on Search Set under the Successive Cancellation List,PSS-SS-SCL)译码算法性能的不足,提出了一种利用增强型奇偶校验码改进PSSSS-SCL译码算法...针对基于路径分裂策略辅助极化码串行抵消列表(Path Splitting Selecting strategy based on Search Set under the Successive Cancellation List,PSS-SS-SCL)译码算法性能的不足,提出了一种利用增强型奇偶校验码改进PSSSS-SCL译码算法的EPC-MS-SCL(Enhanced Parity Check and Monte Carlo Segment aided Successive Cancellation List)译码算法.该算法在极化码编码阶段对信息序列做分段处理,在每段末尾添加增强型奇偶校验码,译码器仅在译码搜索集内元素时进行路径分裂,其余元素直接执行硬判决译码,并在译码完一段序列后立即对该段进行校验,仅保留通过校验的路径,从而减少了错误路径对正确路径的竞争,使正确路径保留到译码结束的概率增加,改善了译码性能,同时减少了译码列表数,使得译码复杂度更低.仿真结果表明,与PSS-SS-SCL译码算法相比较,所提出算法能在一定程度上改善其性能增益且具有更低的译码复杂度.展开更多
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 Sci-tech Innovation Project of Educational Department of Hubei ProvinceMajor Project of Educational Department of Hubei Province (2003A005).
文摘Let W={W(t);t ∈R_+~N} be the d-dimensional N-parameter Brownian Sheet. Sufficient conditions for a compact set F C Rd \ {0} to be a polar set for W are proved. It is also proved that if 2N≤d, then for any compact set E (?)R_>~N ,inf {dimF : F ∈B(Rd), P{W(E) ∩F≠(?)}>0} = d- 2DiroE, and if 2N > d, then for any compact set F C Rd \ {0}, inf{dim E : E ∈ B(R_>~N), P{W(E)∩F≠(?)}>0}=d/2-DimF/2,where B(Rd) and B(R_>~N) denote the Borel σ-algebra in Rd and R_>~N respectively, and dim and Dim are Hausdorff dimension and Packing dimension respectively.
基金supported by the Natural Science Foundation of Zhejiang Province(Y6100663)
文摘This paper studies fractal properties of polar sets for random string processes. We give upper and lower bounds of the hitting probabilities on compact sets and prove some sufficient conditions and necessary conditions for compact sets to be polar for the random string process. Moreover, we also determine the smallest Hausdorff dimensions of non-polar sets by constructing a Cantor-type set to connect its Hausdorff dimension and capacity.
基金the National Natural Science Foundation of China (10471148)the Natural Science Foundation of Shaanxi Province (2005A08, 2006A14)
文摘Let W^-（t）（t∈R＋^N） be the d-dimensional N-parameter generalized Brownian sheet. We study the polar sets for W^-（t）. It is proved that for any α∈ R^d, P{W^-（t） = α, for some t∈ R〉^N} = {1, if βd 〈 2N ,0 if αd〉 2N and the probability that W^-（t） has k-multiple points is 1 or 0 according as whether 2kN〉d（k-1）β or 2kN 〈 d（k - 1）α. These results contain and extend the results of the Brownian sheet, where R〉^N = （0,＋∞）U,R＋^N = [0,＋∞）^N,0〈 α ≤1and β〉1.
基金Key Research Base for Humanities and Social Sciences of Zhejiang Provincial High Education Talents(Statistics of Zhejiang Gongshang University)
文摘Let W^～=^～{W^～（t）; t∈ R＋^N） be a d-dimensional N-parameter generalized Brownian sheet. Necessary and sufficient conditions for a compact set E × F to be a polar set for （t,W^～（t）） are proved. It is also proved that if 2N ≤αd, then for any compact set E ∩→ R〉^N,d-2/α Dim E≤inf{dim F：F∈B（R^d）,P{W^～（E）∩F≠0}〉0}≤d-2/βDimE,and if 2N〉αd, then for any compact set F∪→R^d／{0},α/2（d-DimF）≤inf{dimE：E∈B（R〉^N）,P{W^～（E）∩F≠0}〉0}≤β/2（d-DimF）,where B（R^d） and B（R〉^N） denote the Borel σ-algebra in R^d and in R〉^N respectively, dim and Dim are Hausdorff dimension and Packing dimension respectively.
基金supported by the National Natural Science Foundation of China(Grant No.10471003)Foundation for Authors Awarded Excellent Ph.D.Dissertation.
文摘This paper gives probabilistic expressions of theminimal and maximal positive solutions of the partial differential equation -1/2△v(x) + γ(x)v(x)α = 0 in D, where D is a regular domain in Rd(d ≥ 3) such that its complement Dc is compact, γ(x) is a positive bounded integrable function in D, and 1 ＜α≤ 2. As an application, some necessary and sufficient conditions for a compact set to be S-polar are presented.
基金the National Natural Science Foundation of China and the StateEducation of Commission Ph.D. Station Foundation
文摘The anthem investigate the hitting probability, polarity and the relationship between the polarity and Hausdorff dimension for self-similar Markov processes with state space (0, infinity) and increasing path.
文摘Polar set of Markov processes is an important concept in probabilistic potential theory, but it is not easy to judge the polarity of the sets. In this paper, we give some results which can be easily used to examine the polarity of the sets whenX t belongs to a special class of Levy processes. We also give a result about polar functions of symmetric stable processes.
文摘针对极化码在中短码长时纠错性能的不足,提出了一种基于错误集的极化码改进串行抵消列表(Successive Cancellation List of Polar Codes Based on Error Set,ES-SCL)译码算法。该算法首先根据极化码的信道特性构造错误集,在极化码编码时根据错误集中的元素设置奇偶校验(Parity Check,PC)位,其余位置则放置信息比特和冻结比特,译码器在译码PC位时,每条路径通过校验函数得到PC位的比特估计,不执行路径分裂和剪枝,其余位置则执行SCL译码。仿真结果表明,在加性高斯白噪声信道下,当码长为512,码率为0.5,误块率为10^(-5),最大译码列表数为8时,相较于PC-PSCL译码算法以及CA-SCL译码算法,所提出的ES-SCL译码算法获得了约0.18和0.15 dB的增益;当码长为256,码率为0.5,误码率为10^(-5),最大译码列表数为8时,相较于CA-SCL,PC-PSCL译码算法,获得了约0.3和0.35 dB的增益;此外,采用部分比特分裂译码的ES-SCL译码算法可以在误块率与PC-PSCL译码算法几乎相同的情况下,减少约50%的排序次数,具有更低的译码复杂度。
文摘针对基于路径分裂策略辅助极化码串行抵消列表(Path Splitting Selecting strategy based on Search Set under the Successive Cancellation List,PSS-SS-SCL)译码算法性能的不足,提出了一种利用增强型奇偶校验码改进PSSSS-SCL译码算法的EPC-MS-SCL(Enhanced Parity Check and Monte Carlo Segment aided Successive Cancellation List)译码算法.该算法在极化码编码阶段对信息序列做分段处理,在每段末尾添加增强型奇偶校验码,译码器仅在译码搜索集内元素时进行路径分裂,其余元素直接执行硬判决译码,并在译码完一段序列后立即对该段进行校验,仅保留通过校验的路径,从而减少了错误路径对正确路径的竞争,使正确路径保留到译码结束的概率增加,改善了译码性能,同时减少了译码列表数,使得译码复杂度更低.仿真结果表明,与PSS-SS-SCL译码算法相比较,所提出算法能在一定程度上改善其性能增益且具有更低的译码复杂度.
