Conditioned Brownian motions in bounded domains have been extensively studied.However, we know little about the conditioned processes in an unbounded domain for the difficulty of techniques and methods. Only a few pec...Conditioned Brownian motions in bounded domains have been extensively studied.However, we know little about the conditioned processes in an unbounded domain for the difficulty of techniques and methods. Only a few peculiar cases are investigated. In this note, we shall be devoted to investigating the integrability of the lifetime of conditioned Brownian motions in the angular domain A_m^d={(x^1,…, x^d)∈R^d, x^i】0, 1≤i≤m≤d} (d≥2).展开更多
In this paper, we study the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion （GSDEs） with integral-Lipschitz coefficients.
The backward stochastic differential equations driven by both standard and fractional Brownian motions （or, in short, SFBSDE） axe studied. A Wick-It6 stochastic integral for a fractional Brownian motion is adopted. ...The backward stochastic differential equations driven by both standard and fractional Brownian motions （or, in short, SFBSDE） axe studied. A Wick-It6 stochastic integral for a fractional Brownian motion is adopted. The fractional It6 formula for the standard and fractional Brownian motions is provided. Introducing the concept of the quasi-conditional expectation, we study some its properties. Using the quasi-conditional expectation, we also discuss the existence and uniqueness of solutions to general SFBSDEs, where a fixed point principle is employed. Moreover, solutions to linear SFBSDEs are investigated. Finally, an explicit solution to a class of linear SFBSDEs is found.展开更多
A nonlinear flow of Jeffrey liquid with Cattaneo-Christov heat flux is investigated in the presence of nanoparticles. The features of thermophoretic and Brownian movement are retained. The effects of nonlinear radiati...A nonlinear flow of Jeffrey liquid with Cattaneo-Christov heat flux is investigated in the presence of nanoparticles. The features of thermophoretic and Brownian movement are retained. The effects of nonlinear radiation, magnetohydrodynamic(MHD), and convective conditions are accounted. The conversion of governing equations into ordinary differential equations is prepared via stretching transformations. The consequent equations are solved using the Runge-Kutta-Fehlberg(RKF) method. Impacts of physical constraints on the liquid velocity, the temperature, and the nanoparticle volume fraction are analyzed through graphical illustrations. It is established that the velocity of the liquid and its associated boundary layer width increase with the mixed convection parameter and the Deborah number.展开更多
We establish the moderate deviation for the density process of the single point catalytic super-Brownian motion. The main tools are the abstract Gaertner-Ellis theorem, Dawson-Gaertner the- orem and the contraction pr...We establish the moderate deviation for the density process of the single point catalytic super-Brownian motion. The main tools are the abstract Gaertner-Ellis theorem, Dawson-Gaertner the- orem and the contraction principle. The rate function is expressed by the Fenchel-Legendre transform of log-exponential moment generation function.展开更多
In this paper,a basic estimate for the conditional Riemannian Brownian motion on a complete manifold with non-negative Ricci curvature is established.Applying it to the heat kernel estimate of the operator 1/2△+b,we ...In this paper,a basic estimate for the conditional Riemannian Brownian motion on a complete manifold with non-negative Ricci curvature is established.Applying it to the heat kernel estimate of the operator 1/2△+b,we obtain the Aronson′s estimate for the operator 1/2△+b,which can be regarded as an extension of Peter Li and S.T.Yau's heat kernel estimate for the Laplace-Beltrami operator.展开更多
基金Project supported by the National Natural Science Foundation of China
文摘Conditioned Brownian motions in bounded domains have been extensively studied.However, we know little about the conditioned processes in an unbounded domain for the difficulty of techniques and methods. Only a few peculiar cases are investigated. In this note, we shall be devoted to investigating the integrability of the lifetime of conditioned Brownian motions in the angular domain A_m^d={(x^1,…, x^d)∈R^d, x^i】0, 1≤i≤m≤d} (d≥2).
基金supported by the Major Program in Key Research Institute of Humanities and Social Sciences sponsored by Ministry of Education of China(under grant No.2009JJD790049)the Post-graduate Study Abroad Program sponsored by China Scholarship Council
文摘In this paper, we study the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion （GSDEs） with integral-Lipschitz coefficients.
基金Supported by National Basic Research Program of China (973 Program, No. 2007CB814901)National Natural Science Foundation of China (No. 71171003)+1 种基金Anhui Natural Science Foundation (No. 090416225)Anhui Natural Science Foundation of Universities (No. KJ2010A037)
文摘The backward stochastic differential equations driven by both standard and fractional Brownian motions （or, in short, SFBSDE） axe studied. A Wick-It6 stochastic integral for a fractional Brownian motion is adopted. The fractional It6 formula for the standard and fractional Brownian motions is provided. Introducing the concept of the quasi-conditional expectation, we study some its properties. Using the quasi-conditional expectation, we also discuss the existence and uniqueness of solutions to general SFBSDEs, where a fixed point principle is employed. Moreover, solutions to linear SFBSDEs are investigated. Finally, an explicit solution to a class of linear SFBSDEs is found.
基金University Grant Commission (UGC),New Delhi,for their financial support under National Fellowship for Higher Education (NFHE) of ST students to pursue M.Phil/PhD Degree (F117.1/201516/NFST201517STKAR2228/ (SAIII/Website) Dated:06-April-2016)the Management of Christ University,Bengaluru,India,for the support through Major Research Project to accomplish this research work
文摘A nonlinear flow of Jeffrey liquid with Cattaneo-Christov heat flux is investigated in the presence of nanoparticles. The features of thermophoretic and Brownian movement are retained. The effects of nonlinear radiation, magnetohydrodynamic(MHD), and convective conditions are accounted. The conversion of governing equations into ordinary differential equations is prepared via stretching transformations. The consequent equations are solved using the Runge-Kutta-Fehlberg(RKF) method. Impacts of physical constraints on the liquid velocity, the temperature, and the nanoparticle volume fraction are analyzed through graphical illustrations. It is established that the velocity of the liquid and its associated boundary layer width increase with the mixed convection parameter and the Deborah number.
基金Supported by National Natural Science Foundation of China (Grant No. 11071021)
文摘We establish the moderate deviation for the density process of the single point catalytic super-Brownian motion. The main tools are the abstract Gaertner-Ellis theorem, Dawson-Gaertner the- orem and the contraction principle. The rate function is expressed by the Fenchel-Legendre transform of log-exponential moment generation function.
文摘In this paper,a basic estimate for the conditional Riemannian Brownian motion on a complete manifold with non-negative Ricci curvature is established.Applying it to the heat kernel estimate of the operator 1/2△+b,we obtain the Aronson′s estimate for the operator 1/2△+b,which can be regarded as an extension of Peter Li and S.T.Yau's heat kernel estimate for the Laplace-Beltrami operator.
