In this paper, we consider the local time and the self-intersection local time for a bifractional Brownian motion, and the collision local time for two independent bifractional Brownian motions. We mainly prove the ex...In this paper, we consider the local time and the self-intersection local time for a bifractional Brownian motion, and the collision local time for two independent bifractional Brownian motions. We mainly prove the existence and smoothness of the self-intersection local time and the collision local time, through the strong local nondeterminism of bifractional Brownian motion, L2 convergence and Chaos expansion.展开更多
Let X = {X(t), t ∈ ? N } be a Gaussian random field with values in ? d defined by (1) $$ X(t) = (X_1 (t),...,X_d (t)),\forall t \in \mathbb{R}^N . $$ . The properties of space and time anisotropy of X and their conne...Let X = {X(t), t ∈ ? N } be a Gaussian random field with values in ? d defined by (1) $$ X(t) = (X_1 (t),...,X_d (t)),\forall t \in \mathbb{R}^N . $$ . The properties of space and time anisotropy of X and their connections to uniform Hausdorff dimension results are discussed. It is shown that in general the uniform Hausdorff dimension result does not hold for the image sets of a space-anisotropic Gaussian random field X.When X is an (N, d)-Gaussian random field as in (1), where X 1,...,X d are independent copies of a real valued, centered Gaussian random field X 0 which is anisotropic in the time variable. We establish uniform Hausdorff dimension results for the image sets of X. These results extend the corresponding results on one-dimensional Brownian motion, fractional Brownian motion and the Brownian sheet.展开更多
There are many variants of Petri net at present, and some of them can be used to model system with both function and performance specification, such as stochastic Petri net, generalized stochastic Petri net and probab...There are many variants of Petri net at present, and some of them can be used to model system with both function and performance specification, such as stochastic Petri net, generalized stochastic Petri net and probabilistic Petri net. In this paper, we utilize extended Petri net to address the issue of modeling and verifying system with probability and nondeterminism besides function aspects. Using probabilistic Petri net as reference, we propose a new mixed model NPPN （Nondeterministic Probabilistic Petri Net） system, which can model and verify systems with qualitative and quantitative behaviours. Then we develop a kind of process algebra for NPPN system to interpret its algebraic semantics, and an action- based PCTL （Probabilistic Computation Tree Logic） to interpret its logical semantics. Afterwards we present the rules for compositional operation of NPPN system based on NPPN system process algebra, and the model checking algorithm based on the action-based PCTL. In order to put the NPPN system into practice, we develop a friendly and visual tool for modeling, analyzing, simulating, and verifying NPPN system using action-based PCTL. The usefulness and effectiveness of the NPPN system are illustrated by modeling and model checking an elaborate model of travel arrangements workflow.展开更多
对具有不确定性的复杂系统如网络协议等的性能进行分析是当前的研究热点.将空间资源分析纳入到性能评估过程,用模型检测技术验证时间或空间性能是否满足期望的需求约束.用能刻画不确定性的连续时间Markov回报过程(Continuous-Ti me Mark...对具有不确定性的复杂系统如网络协议等的性能进行分析是当前的研究热点.将空间资源分析纳入到性能评估过程,用模型检测技术验证时间或空间性能是否满足期望的需求约束.用能刻画不确定性的连续时间Markov回报过程(Continuous-Ti me Markov Reward Process,CTMRP)作为时间或空间性能验证模型;用正则式表示路径约束,扩展连续随机回报逻辑CSRL(Continuous Stochastic Reward Logic)的时态路径算子,用以刻画更加广泛的基于状态或路径的时间或空间性能验证属性;提出并证明CTMRP在确定性策略下空间时间可达概率的对偶性质,将带有约束的空间性能验证最终转化为时间性能的可达分析,给出验证算法.文中的结论和算法为复杂系统的性能分析提供了新的思路和方法.展开更多
Unpredictable and irreproducible digital keys are required to modulate security-related information in secure communication systems.True random number generators(TRNGs)rather than pseudorandom number generators(PRNGs)...Unpredictable and irreproducible digital keys are required to modulate security-related information in secure communication systems.True random number generators(TRNGs)rather than pseudorandom number generators(PRNGs)are required for the highest level of security.TRNG is a significant component in the digital security realm for extracting unpredictable binary bitstreams.Presently,most TRNGs extract high-quality“noise”from unpredictable physical random phenomena.Thus,these applications must be equipped with external hardware for collecting entropy and converting them into a random digital sequence.This study introduces a lightweight and efficient true random number generator(LETRNG)that uses the inherent randomness of a central processing unit(CPU)and an operating system(OS)as the source of entropy.We then utilize a lightweight post-processing method based on XOR and fair coin operation to generate an unbiased random binary sequence.Evaluations based on two famous test suites(NIST and ENT)show that LETRNG is perfectly capable of generating high-quality random numbers suitable for various GNU/Linux systems.展开更多
Let B^α = {B^α（t）,t E R^N} be an （N,d）-fractional Brownian motion with Hurst index α∈ （0, 1）. By applying the strong local nondeterminism of B^α, we prove certain forms of uniform Hausdorff dimension result...Let B^α = {B^α（t）,t E R^N} be an （N,d）-fractional Brownian motion with Hurst index α∈ （0, 1）. By applying the strong local nondeterminism of B^α, we prove certain forms of uniform Hausdorff dimension results for the images of B^α when N 〉 αd. Our results extend those of Kaufman for one-dimensional Brownian motion.展开更多
Let X^H(u)(u)={X^H(u)(u);u∈R^N+}be linear multifractional stable sheets with index functional H(u),where H(u)=(H1(u),…,HN(u))is a function with values in(0;1)N.Based on some assumptions of H(u),we obtain the existen...Let X^H(u)(u)={X^H(u)(u);u∈R^N+}be linear multifractional stable sheets with index functional H(u),where H(u)=(H1(u),…,HN(u))is a function with values in(0;1)N.Based on some assumptions of H(u),we obtain the existence of the local times of X^H(u)(u)and establish its joint continuity and the Holder regularity.These results generalize the corresponding results about fractional stable sheets to multifractional stable sheets.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10871103)
文摘In this paper, we consider the local time and the self-intersection local time for a bifractional Brownian motion, and the collision local time for two independent bifractional Brownian motions. We mainly prove the existence and smoothness of the self-intersection local time and the collision local time, through the strong local nondeterminism of bifractional Brownian motion, L2 convergence and Chaos expansion.
基金supported by National Science Foundation of the United States (Grant No.DMS-0706728)
文摘Let X = {X(t), t ∈ ? N } be a Gaussian random field with values in ? d defined by (1) $$ X(t) = (X_1 (t),...,X_d (t)),\forall t \in \mathbb{R}^N . $$ . The properties of space and time anisotropy of X and their connections to uniform Hausdorff dimension results are discussed. It is shown that in general the uniform Hausdorff dimension result does not hold for the image sets of a space-anisotropic Gaussian random field X.When X is an (N, d)-Gaussian random field as in (1), where X 1,...,X d are independent copies of a real valued, centered Gaussian random field X 0 which is anisotropic in the time variable. We establish uniform Hausdorff dimension results for the image sets of X. These results extend the corresponding results on one-dimensional Brownian motion, fractional Brownian motion and the Brownian sheet.
基金This work was supported by the National Natural Science Foundation of China under Grant Nos. 60970007, 61073050 and 61170044, the National Basic Research 973 Program of China under Grant No. 2007CB310800, the Shanghai Leading Academic Discipline Project of China under Grant No. J50103, and the Natural Science Foundation of Shandong Province of China under Grant No. ZR2012FQ013.
文摘There are many variants of Petri net at present, and some of them can be used to model system with both function and performance specification, such as stochastic Petri net, generalized stochastic Petri net and probabilistic Petri net. In this paper, we utilize extended Petri net to address the issue of modeling and verifying system with probability and nondeterminism besides function aspects. Using probabilistic Petri net as reference, we propose a new mixed model NPPN （Nondeterministic Probabilistic Petri Net） system, which can model and verify systems with qualitative and quantitative behaviours. Then we develop a kind of process algebra for NPPN system to interpret its algebraic semantics, and an action- based PCTL （Probabilistic Computation Tree Logic） to interpret its logical semantics. Afterwards we present the rules for compositional operation of NPPN system based on NPPN system process algebra, and the model checking algorithm based on the action-based PCTL. In order to put the NPPN system into practice, we develop a friendly and visual tool for modeling, analyzing, simulating, and verifying NPPN system using action-based PCTL. The usefulness and effectiveness of the NPPN system are illustrated by modeling and model checking an elaborate model of travel arrangements workflow.
基金This work was partially supported by National Key R&D Program of China(No.2020YFC0832500)Fundamental Research Funds for the Central Universities(Nos.lzujbky-2021-sp47,lzujbky-2020-sp02,lzujbky-2019-kb51,and lzujbky2018-k12)the National Natural Science Foundation of China(No.61402210).We also gratefully acknowledge the support of NVIDIA Corporation with the donation of the Jetson-TX1 used for this research.
文摘Unpredictable and irreproducible digital keys are required to modulate security-related information in secure communication systems.True random number generators(TRNGs)rather than pseudorandom number generators(PRNGs)are required for the highest level of security.TRNG is a significant component in the digital security realm for extracting unpredictable binary bitstreams.Presently,most TRNGs extract high-quality“noise”from unpredictable physical random phenomena.Thus,these applications must be equipped with external hardware for collecting entropy and converting them into a random digital sequence.This study introduces a lightweight and efficient true random number generator(LETRNG)that uses the inherent randomness of a central processing unit(CPU)and an operating system(OS)as the source of entropy.We then utilize a lightweight post-processing method based on XOR and fair coin operation to generate an unbiased random binary sequence.Evaluations based on two famous test suites(NIST and ENT)show that LETRNG is perfectly capable of generating high-quality random numbers suitable for various GNU/Linux systems.
基金Research partially supported by NSF Grant DMS-0404729
文摘Let B^α = {B^α（t）,t E R^N} be an （N,d）-fractional Brownian motion with Hurst index α∈ （0, 1）. By applying the strong local nondeterminism of B^α, we prove certain forms of uniform Hausdorff dimension results for the images of B^α when N 〉 αd. Our results extend those of Kaufman for one-dimensional Brownian motion.
文摘Let X^H(u)(u)={X^H(u)(u);u∈R^N+}be linear multifractional stable sheets with index functional H(u),where H(u)=(H1(u),…,HN(u))is a function with values in(0;1)N.Based on some assumptions of H(u),we obtain the existence of the local times of X^H(u)(u)and establish its joint continuity and the Holder regularity.These results generalize the corresponding results about fractional stable sheets to multifractional stable sheets.
