We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),...We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),their local times exist when d≤3.A Tanaka formula of the local time is also derived.展开更多
In this article, we consider the continuous gas in a bounded domain ∧ of R^＋ or R^d described by a Gibbsian probability measure μη∧ associated with a pair interaction φ, the inverse temperature β, the activity...In this article, we consider the continuous gas in a bounded domain ∧ of R^＋ or R^d described by a Gibbsian probability measure μη∧ associated with a pair interaction φ, the inverse temperature β, the activity z 〉 0, and the boundary condition η. Define F ∫ωf（s）wA（ds）. Applying the generalized Ito＇s formula for forward-backward martingales （see Klein et M. [5]）, we obtain convex concentration inequalities for F with respect to the Gibbs measure μη∧. On the other hand, by FKG inequality on the Poisson space, we also give a new simple argument for the stochastic domination for the Gibbs measure.展开更多
In this paper,we consider the measure determined by a fractional OrnsteinUhlenbeck process.For such a measure,we establish an explicit form of the martingale representation theorem and consequently obtain an explicit ...In this paper,we consider the measure determined by a fractional OrnsteinUhlenbeck process.For such a measure,we establish an explicit form of the martingale representation theorem and consequently obtain an explicit form of the Logarithmic-Sobolev inequality.To this end,we also present the integration by parts formula for such a measure,which is obtained via its pull back formula and the Bismut method.展开更多
We build Wiener measure for the path space on the Heisenberg group by using of the heat kernel corresponding to the sub-Laplacian and give the definition of the Wiener integral.Then we give the FeynmanKac formula.
Shannon’s information measure is a crucial concept in Information Theory. And the research, for the mathematics structure of Shannon’s information measure, is to recognize the essence of information measure. The lin...Shannon’s information measure is a crucial concept in Information Theory. And the research, for the mathematics structure of Shannon’s information measure, is to recognize the essence of information measure. The linear relation between Shannon’s information measures and some signed measure space by using the formal symbols substitution rule is discussed. Furthermore, the coefficient matrix recurrent formula of the linear relation is obtained. Then the coefficient matrix is proved to be invertible via mathematical induction. This shows that the linear relation is one-to-one, and according to this, it can be concluded that a compact space can be generated from Shannon’s information measures.展开更多
The present note is a continuation of [1]. We will give a method for calculating the Skorohod integrals and the concept of stochastic derivatives for random fields. Based on them, some kind of generalization of It for...The present note is a continuation of [1]. We will give a method for calculating the Skorohod integrals and the concept of stochastic derivatives for random fields. Based on them, some kind of generalization of It formula is presented here. The readers are referred to [1] for necessary definitions and notations.展开更多
In this article, we give a new proof of the Itôformula for some integral processes related to the space-time Lévy noise introduced in [1] [2] as an alternative for the Gaussian white noise perturbing an...In this article, we give a new proof of the Itôformula for some integral processes related to the space-time Lévy noise introduced in [1] [2] as an alternative for the Gaussian white noise perturbing an SPDE. We discuss two applications of this result, which are useful in the study of SPDEs driven by a space-time Lévy noise with finite variance: a maximal inequality for the p-th moment of the stochastic integral, and the Itôrepresentation theorem leading to a chaos expansion similar to the Gaussian case.展开更多
基金Partial funding in support of this work was provided by the Natural Sciences and Engineering Research Council of Canada(NSERC)the Department of Mathematics at the University of Oregon。
文摘We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),their local times exist when d≤3.A Tanaka formula of the local time is also derived.
文摘In this article, we consider the continuous gas in a bounded domain ∧ of R^＋ or R^d described by a Gibbsian probability measure μη∧ associated with a pair interaction φ, the inverse temperature β, the activity z 〉 0, and the boundary condition η. Define F ∫ωf（s）wA（ds）. Applying the generalized Ito＇s formula for forward-backward martingales （see Klein et M. [5]）, we obtain convex concentration inequalities for F with respect to the Gibbs measure μη∧. On the other hand, by FKG inequality on the Poisson space, we also give a new simple argument for the stochastic domination for the Gibbs measure.
基金supported by the National Natural Science Foundation of China(11801064)。
文摘In this paper,we consider the measure determined by a fractional OrnsteinUhlenbeck process.For such a measure,we establish an explicit form of the martingale representation theorem and consequently obtain an explicit form of the Logarithmic-Sobolev inequality.To this end,we also present the integration by parts formula for such a measure,which is obtained via its pull back formula and the Bismut method.
基金supported by National Natural Science Foundation of China (Grant No. 10990012)50-Class General Financial Grant from the China Postdoctoral Science Foundation (Grant No. 2011M501317)
文摘We build Wiener measure for the path space on the Heisenberg group by using of the heat kernel corresponding to the sub-Laplacian and give the definition of the Wiener integral.Then we give the FeynmanKac formula.
基金the Science and Technology Research Project of Education Department, Heilongjiang Province (Grant No.11513095)the Science andTechnology Foundation of Heilongjiang Institute of Science and Technology(Grant No.04 -25).
文摘Shannon’s information measure is a crucial concept in Information Theory. And the research, for the mathematics structure of Shannon’s information measure, is to recognize the essence of information measure. The linear relation between Shannon’s information measures and some signed measure space by using the formal symbols substitution rule is discussed. Furthermore, the coefficient matrix recurrent formula of the linear relation is obtained. Then the coefficient matrix is proved to be invertible via mathematical induction. This shows that the linear relation is one-to-one, and according to this, it can be concluded that a compact space can be generated from Shannon’s information measures.
基金Project partially supported by the National Natural Science Foundation of China
文摘The present note is a continuation of [1]. We will give a method for calculating the Skorohod integrals and the concept of stochastic derivatives for random fields. Based on them, some kind of generalization of It formula is presented here. The readers are referred to [1] for necessary definitions and notations.
基金funded by a grant from the Natural Sciences and Engineering Research Council of Canada.
文摘In this article, we give a new proof of the Itôformula for some integral processes related to the space-time Lévy noise introduced in [1] [2] as an alternative for the Gaussian white noise perturbing an SPDE. We discuss two applications of this result, which are useful in the study of SPDEs driven by a space-time Lévy noise with finite variance: a maximal inequality for the p-th moment of the stochastic integral, and the Itôrepresentation theorem leading to a chaos expansion similar to the Gaussian case.
