In the present paper,we mostly focus on P_(p)^(2)-statistical convergence.We will look into the uniform integrability via the power series method and its characterizations for double sequences.Also,the notions of P_(p...In the present paper,we mostly focus on P_(p)^(2)-statistical convergence.We will look into the uniform integrability via the power series method and its characterizations for double sequences.Also,the notions of P_(p)^(2)-statistically Cauchy sequence,P_(p)^(2)-statistical boundedness and core for double sequences will be described in addition to these findings.展开更多
Let x （xn）≥1 be a martingale on a noncommutative probability space n （M, r） and （wn）n≥1 a sequence of positive numbers such that Wn = ∑ k=1^n wk →∞ as n →∞ We prove that x = （x.）n≥1 converges in E（M...Let x （xn）≥1 be a martingale on a noncommutative probability space n （M, r） and （wn）n≥1 a sequence of positive numbers such that Wn = ∑ k=1^n wk →∞ as n →∞ We prove that x = （x.）n≥1 converges in E（M） if and only if （σn（x）n≥1 converges in E（.hd）, where E（A//） is a noncommutative rearrangement invariant Banach function space with the Fatou property and σn（x） is given by σn（x） = 1/Wn ∑k=1^n wkxk, n=1, 2, .If in addition, E（Ad） has absolutely continuous norm, then, （an（x））≥1 converges in E（.M） if and only if x = （Xn）n≥1 is uniformly integrable and its limit in measure topology x∞∈ E（M）.展开更多
For weighted sums of the form?j=1kn anj Xnj\sum{_{j=1}^{k_(n)}}a_({nj})X_({nj})where{a_(nj),1?j?k_(n)↑∞,n?1}is a real constant array and{X_(aj),1≤j≤k n,n≥1}is a rowwise independent,zero mean,random element array ...For weighted sums of the form?j=1kn anj Xnj\sum{_{j=1}^{k_(n)}}a_({nj})X_({nj})where{a_(nj),1?j?k_(n)↑∞,n?1}is a real constant array and{X_(aj),1≤j≤k n,n≥1}is a rowwise independent,zero mean,random element array in a real separable Banach space of typep,we establishL r convergence theorem and a general weak law of large numbers respectively,conversely,we characterize Banach spaces of typep in terms of convergence inr-th mean and probability for such weighted sums.展开更多
In this paper,we extend the equivalence of the analytic and probabilistic notions of harmonicity in the context of Hunt processes associated with non-symmetric Dirichlet forms on locally compact separable metric space...In this paper,we extend the equivalence of the analytic and probabilistic notions of harmonicity in the context of Hunt processes associated with non-symmetric Dirichlet forms on locally compact separable metric spaces.Extensions to the processes associated with semi-Dirichlet forms and nearly symmetric right processes on Lusin spaces including infinite dimensional spaces are mentioned at the end of this paper.展开更多
Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges...Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges bilaterally almost uniformly （b.a.u.） if and only if the weighted average （σan（x））n≥1 of x converges b.a.u, to the same limit under some condition, where σn（x） is given by σn（x）=1/Wn ^n∑_k=1 wkxk,n=1,2,… Furthermore, we prove that x = （xn）n≥1 converges in Lp（М） if and only if （σ＇n（x））n≥1 converges in Lp（М）, where 1 ≤p 〈 ∞ .We also get a criterion of uniform integrability for a family in L1（М）.展开更多
X charts with estimated control limits are commonly used in practice and treated as if the in-control process parameters were known. However, the former can behave quite differently from the latter. To understand the ...X charts with estimated control limits are commonly used in practice and treated as if the in-control process parameters were known. However, the former can behave quite differently from the latter. To understand the differences, it is necessary to study the run length distribution (RLD), its mean (ARL) and standard deviation (SDRL) of the X charts when the control limits are estimated. However, ARL and SDRL are integrals over an infinite region with a boundless integrand, the finiteness has not been proved in literature. In this paper, we show the finiteness and uniform integrability of ARL and SDRL. Furthermore, we numerically evaluate the ARL, SDRL and the RLD using number theory method. A numerical study is conducted to assess the performance of the proposed method and the results are compared with those given by Quesenberry and Chen.展开更多
In space-air-ground uniformly integrated network(SAGUIN),a centralized data control center(DCC)is deployed to manage the shared spectrum resources across the space,aerial,and ground layers under a unified communicatio...In space-air-ground uniformly integrated network(SAGUIN),a centralized data control center(DCC)is deployed to manage the shared spectrum resources across the space,aerial,and ground layers under a unified communication architecture,which makes it a promising candidate for the next-generation wireless systems.However,due to the extremely large physical scale of SAGUIN,signals transmitted across different layers experience substantially different propagation delays and channel conditions,a disparity further amplified by the network's layered structure and spatially clustered topology.On the other hand,task-oriented communications typically employ short-packet transmissions,whose durations are only a small fraction of the largepropagation delays between satellites,aerial platforms,and ground users.The above phenomena,including asynchronous and out-of-order signal arrivals induced by delay asymmetry among satellites,aerial platforms,and ground users;non-coherent transmissions over heterogeneous links with substantial timing offsets;and spatiotemporally coupled interferences arising from overlapping coverage areas and disparities in propagation delay,present major challenges for throughput modeling,access protocol design,and network resource management.In this article,we analyze the network throughput,design the multi-user access signal detection scheme,and optimize the task scheduling under ripple effect,thereby offering new insights into the deployment of future SAGUINs.展开更多
In this paper we shall characterize the large deviation principles(abbreviated to LDP) of Donsker-Varadhan of a Markov process both for the weak convergence topology and for theτ- topology,by means of a hyper-exponen...In this paper we shall characterize the large deviation principles(abbreviated to LDP) of Donsker-Varadhan of a Markov process both for the weak convergence topology and for theτ- topology,by means of a hyper-exponential recurrence property.A Lyapunov criterion for this type of recurrence property is presented.These results are applied to countable Markov chains,unidimensional diffusions,elliptic or hypoelliptic diffusions on Riemannian manifolds.Several counter-examples are equally presented.展开更多
文摘In the present paper,we mostly focus on P_(p)^(2)-statistical convergence.We will look into the uniform integrability via the power series method and its characterizations for double sequences.Also,the notions of P_(p)^(2)-statistically Cauchy sequence,P_(p)^(2)-statistical boundedness and core for double sequences will be described in addition to these findings.
基金supported by the National Natural Science Foundation of China (11071190)
文摘Let x （xn）≥1 be a martingale on a noncommutative probability space n （M, r） and （wn）n≥1 a sequence of positive numbers such that Wn = ∑ k=1^n wk →∞ as n →∞ We prove that x = （x.）n≥1 converges in E（M） if and only if （σn（x）n≥1 converges in E（.hd）, where E（A//） is a noncommutative rearrangement invariant Banach function space with the Fatou property and σn（x） is given by σn（x） = 1/Wn ∑k=1^n wkxk, n=1, 2, .If in addition, E（Ad） has absolutely continuous norm, then, （an（x））≥1 converges in E（.M） if and only if x = （Xn）n≥1 is uniformly integrable and its limit in measure topology x∞∈ E（M）.
基金Supported by the National Natural Science F oundation of China(No.10071058)
文摘For weighted sums of the form?j=1kn anj Xnj\sum{_{j=1}^{k_(n)}}a_({nj})X_({nj})where{a_(nj),1?j?k_(n)↑∞,n?1}is a real constant array and{X_(aj),1≤j≤k n,n≥1}is a rowwise independent,zero mean,random element array in a real separable Banach space of typep,we establishL r convergence theorem and a general weak law of large numbers respectively,conversely,we characterize Banach spaces of typep in terms of convergence inr-th mean and probability for such weighted sums.
基金supported by National Natural Science Foundation of China(Grant No.10721101)National Basic Research Program of China(Grant No.2006CB805900)+1 种基金Key Lab of Random Complex Structures and Data Science,Chinese Academy of Sciences(Grant No.2008DP173182)Sino-Germany IGK Project
文摘In this paper,we extend the equivalence of the analytic and probabilistic notions of harmonicity in the context of Hunt processes associated with non-symmetric Dirichlet forms on locally compact separable metric spaces.Extensions to the processes associated with semi-Dirichlet forms and nearly symmetric right processes on Lusin spaces including infinite dimensional spaces are mentioned at the end of this paper.
基金supported by National Natural Science Foundation of China (Grant No.11071190)
文摘Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges bilaterally almost uniformly （b.a.u.） if and only if the weighted average （σan（x））n≥1 of x converges b.a.u, to the same limit under some condition, where σn（x） is given by σn（x）=1/Wn ^n∑_k=1 wkxk,n=1,2,… Furthermore, we prove that x = （xn）n≥1 converges in Lp（М） if and only if （σ＇n（x））n≥1 converges in Lp（М）, where 1 ≤p 〈 ∞ .We also get a criterion of uniform integrability for a family in L1（М）.
基金This research is is partially supported by the National Natural Science Foundation of China.
文摘X charts with estimated control limits are commonly used in practice and treated as if the in-control process parameters were known. However, the former can behave quite differently from the latter. To understand the differences, it is necessary to study the run length distribution (RLD), its mean (ARL) and standard deviation (SDRL) of the X charts when the control limits are estimated. However, ARL and SDRL are integrals over an infinite region with a boundless integrand, the finiteness has not been proved in literature. In this paper, we show the finiteness and uniform integrability of ARL and SDRL. Furthermore, we numerically evaluate the ARL, SDRL and the RLD using number theory method. A numerical study is conducted to assess the performance of the proposed method and the results are compared with those given by Quesenberry and Chen.
基金supported by the National Natural Science Foundation of China under Grant 62341112.
文摘In space-air-ground uniformly integrated network(SAGUIN),a centralized data control center(DCC)is deployed to manage the shared spectrum resources across the space,aerial,and ground layers under a unified communication architecture,which makes it a promising candidate for the next-generation wireless systems.However,due to the extremely large physical scale of SAGUIN,signals transmitted across different layers experience substantially different propagation delays and channel conditions,a disparity further amplified by the network's layered structure and spatially clustered topology.On the other hand,task-oriented communications typically employ short-packet transmissions,whose durations are only a small fraction of the largepropagation delays between satellites,aerial platforms,and ground users.The above phenomena,including asynchronous and out-of-order signal arrivals induced by delay asymmetry among satellites,aerial platforms,and ground users;non-coherent transmissions over heterogeneous links with substantial timing offsets;and spatiotemporally coupled interferences arising from overlapping coverage areas and disparities in propagation delay,present major challenges for throughput modeling,access protocol design,and network resource management.In this article,we analyze the network throughput,design the multi-user access signal detection scheme,and optimize the task scheduling under ripple effect,thereby offering new insights into the deployment of future SAGUINs.
基金This work is partially supported by the NSF of China and the Foundation of Y.D.Fok.
文摘In this paper we shall characterize the large deviation principles(abbreviated to LDP) of Donsker-Varadhan of a Markov process both for the weak convergence topology and for theτ- topology,by means of a hyper-exponential recurrence property.A Lyapunov criterion for this type of recurrence property is presented.These results are applied to countable Markov chains,unidimensional diffusions,elliptic or hypoelliptic diffusions on Riemannian manifolds.Several counter-examples are equally presented.
