In this paper by Sobolev imbedding theorem and characterization theorem of generalized operators the existence of P(φ)2 quantum fields as generalized operators is obtained and a rigorous mathematical interpretation o...In this paper by Sobolev imbedding theorem and characterization theorem of generalized operators the existence of P(φ)2 quantum fields as generalized operators is obtained and a rigorous mathematical interpretation of renormalization procedure is given under white noise theory.展开更多
In this paper we prove the pathwise uniqueness of a kind of two-parameter Volterra type stochastic differential equations under the coefficients satisfy the non-Lipschitz conditions. We use a martingale formula in ste...In this paper we prove the pathwise uniqueness of a kind of two-parameter Volterra type stochastic differential equations under the coefficients satisfy the non-Lipschitz conditions. We use a martingale formula in stead of Ito formula, which leads to simplicity the process of proof and extends the result to unbounded coefficients case.展开更多
Under the framework of white noise analysis, the existence of scattering solutions to the abstract dynamical φ4^4 wave equations in terms of generalized operators （see Section 3 below） is proven via a combination o...Under the framework of white noise analysis, the existence of scattering solutions to the abstract dynamical φ4^4 wave equations in terms of generalized operators （see Section 3 below） is proven via a combination of the characterization for the symbol of generalized operators and the classical scattering results. In addition, some properties （Poincare invariance and irreducibility） of the solutions are discussed.展开更多
In this article,we study the hitting probabilities of weighted Poisson processes and their subordinated versions with different intensities.Furthermore,we simulate and analyze the asymptotic properties of the hitting ...In this article,we study the hitting probabilities of weighted Poisson processes and their subordinated versions with different intensities.Furthermore,we simulate and analyze the asymptotic properties of the hitting probabilities in different weights and give an example in the case of subordination.展开更多
基金Project supported by NSFC (10171035) and Hubei University Youth Foundation (97A012)
文摘In this paper by Sobolev imbedding theorem and characterization theorem of generalized operators the existence of P(φ)2 quantum fields as generalized operators is obtained and a rigorous mathematical interpretation of renormalization procedure is given under white noise theory.
基金Foundation item: Hubei University Youngth Foundations (099206).
文摘In this paper we prove the pathwise uniqueness of a kind of two-parameter Volterra type stochastic differential equations under the coefficients satisfy the non-Lipschitz conditions. We use a martingale formula in stead of Ito formula, which leads to simplicity the process of proof and extends the result to unbounded coefficients case.
基金supported by NSFC (10401011,10871153)China Postdoctoral Science Foundation (2005037660)
文摘Under the framework of white noise analysis, the existence of scattering solutions to the abstract dynamical φ4^4 wave equations in terms of generalized operators （see Section 3 below） is proven via a combination of the characterization for the symbol of generalized operators and the classical scattering results. In addition, some properties （Poincare invariance and irreducibility） of the solutions are discussed.
基金supported by the National Natural Science Foundation of China(11571262,11731012 and 11971361)。
文摘In this article,we study the hitting probabilities of weighted Poisson processes and their subordinated versions with different intensities.Furthermore,we simulate and analyze the asymptotic properties of the hitting probabilities in different weights and give an example in the case of subordination.
