In this paper,we shall exploit the Freud method in the Classical operator approximation theory to im- prove known quantitative estimalions with an emphasis on Calculah' on the generic constants.
In this paper we obtained general representation formulae for strongly continuous cosine operator functions via probabilistic approach,which include Webb's[1]and Shaw's[2]formulae and some new one as special c...In this paper we obtained general representation formulae for strongly continuous cosine operator functions via probabilistic approach,which include Webb's[1]and Shaw's[2]formulae and some new one as special cases.We also give the quantitative estimations for the general formulae.展开更多
This paper explores the diffeomorphism of a backward stochastic ordinary differential equation (BSDE) to a system of semi-linear backward stochastic partial differential equations (BSPDEs), under the inverse of a stoc...This paper explores the diffeomorphism of a backward stochastic ordinary differential equation (BSDE) to a system of semi-linear backward stochastic partial differential equations (BSPDEs), under the inverse of a stochastic flow generated by an ordinary stochastic differential equation (SDE). The author develops a new approach to BSPDEs and also provides some new results. The adapted solution of BSPDEs in terms of those of SDEs and BSDEs is constructed. This brings a new insight on BSPDEs, and leads to a probabilistic approach. As a consequence, the existence, uniqueness, and regularity results are obtained for the (classical, Sobolev, and distributional) solution of BSPDEs.The dimension of the space variable x is allowed to be arbitrary n, and BSPDEs are allowed to be nonlinear in both unknown variables, which implies that the BSPDEs may be nonlinear in the gradient. Due to the limitation of space, however, this paper concerns only classical solution of BSPDEs under some more restricted assumptions.展开更多
In this paper,the authors consider a reflected backward stochastic differential equation driven by a G-Brownian motion(G-BSDE for short),with the generator growing quadratically in the second unknown.The authors obtai...In this paper,the authors consider a reflected backward stochastic differential equation driven by a G-Brownian motion(G-BSDE for short),with the generator growing quadratically in the second unknown.The authors obtain the existence by the penalty method,and some a priori estimates which imply the uniqueness,for solutions of the G-BSDE.Moreover,focusing their discussion at the Markovian setting,the authors give a nonlinear Feynman-Kac formula for solutions of a fully nonlinear partial differential equation.展开更多
文摘In this paper,we shall exploit the Freud method in the Classical operator approximation theory to im- prove known quantitative estimalions with an emphasis on Calculah' on the generic constants.
文摘In this paper we obtained general representation formulae for strongly continuous cosine operator functions via probabilistic approach,which include Webb's[1]and Shaw's[2]formulae and some new one as special cases.We also give the quantitative estimations for the general formulae.
基金Project supported by the National Natural Science Foundation of China (No.10325101, No.101310310)the Science Foundation of the Ministry of Education of China (No. 20030246004).
文摘This paper explores the diffeomorphism of a backward stochastic ordinary differential equation (BSDE) to a system of semi-linear backward stochastic partial differential equations (BSPDEs), under the inverse of a stochastic flow generated by an ordinary stochastic differential equation (SDE). The author develops a new approach to BSPDEs and also provides some new results. The adapted solution of BSPDEs in terms of those of SDEs and BSDEs is constructed. This brings a new insight on BSPDEs, and leads to a probabilistic approach. As a consequence, the existence, uniqueness, and regularity results are obtained for the (classical, Sobolev, and distributional) solution of BSPDEs.The dimension of the space variable x is allowed to be arbitrary n, and BSPDEs are allowed to be nonlinear in both unknown variables, which implies that the BSPDEs may be nonlinear in the gradient. Due to the limitation of space, however, this paper concerns only classical solution of BSPDEs under some more restricted assumptions.
基金supported by the National Science Foundation of China(No.11631004)the Science and Technology Commission of Shanghai Municipality(No.14XD1400400).
文摘In this paper,the authors consider a reflected backward stochastic differential equation driven by a G-Brownian motion(G-BSDE for short),with the generator growing quadratically in the second unknown.The authors obtain the existence by the penalty method,and some a priori estimates which imply the uniqueness,for solutions of the G-BSDE.Moreover,focusing their discussion at the Markovian setting,the authors give a nonlinear Feynman-Kac formula for solutions of a fully nonlinear partial differential equation.
