A multi-dimensional version of the duality principle of Sawyer type [1] is obtained whenever the corresponding weight satisfies some doubling property.
We study the existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations(BSVIEs)with jumps,where path-dependence means the dependence of the free term and generator of a pa...We study the existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations(BSVIEs)with jumps,where path-dependence means the dependence of the free term and generator of a path of a c`adl`ag process.Furthermore,we prove path-differentiability of such a solution and establish the duality principle between a linear path-dependent forward stochastic Volterra integral equation(FSVIE)with jumps and a linear path-dependent BSVIE with jumps.As a result of the duality principle we get a comparison theorem and derive a class of dynamic coherent risk measures based on path-dependent BSVIEs with jumps.展开更多
On the basis of composition duality principles, augmented three-field macrohybrid mixed variational problems and finite element schemes are analyzed. The compatibility condition adopted here, for compositional dualiza...On the basis of composition duality principles, augmented three-field macrohybrid mixed variational problems and finite element schemes are analyzed. The compatibility condition adopted here, for compositional dualization, is the coupling operator surjectivity, property that expresses in a general operator sense the Ladysenskaja-Babulka-Brezzi inf-sup condition. Variational macro-hybridization is performed under the assumption of decomposable primal and dual spaces relative to nonoverlapping domain decompositions. Then, through compositional dualization macro-hybrid mixed problems are obtained, with internal boundary dual traces as Lagrange multipliers. Also, ＂mass＂ preconditioned aug- mentation of three-field formulations are derived, stabilizing macro-hybrid mixed finite element schemes and rendering possible speed up of rates of convergence. Dual mixed incompressible Darcy flow problems illustrate the theory throughout the paper.展开更多
文摘A multi-dimensional version of the duality principle of Sawyer type [1] is obtained whenever the corresponding weight satisfies some doubling property.
文摘We study the existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations(BSVIEs)with jumps,where path-dependence means the dependence of the free term and generator of a path of a c`adl`ag process.Furthermore,we prove path-differentiability of such a solution and establish the duality principle between a linear path-dependent forward stochastic Volterra integral equation(FSVIE)with jumps and a linear path-dependent BSVIE with jumps.As a result of the duality principle we get a comparison theorem and derive a class of dynamic coherent risk measures based on path-dependent BSVIEs with jumps.
文摘On the basis of composition duality principles, augmented three-field macrohybrid mixed variational problems and finite element schemes are analyzed. The compatibility condition adopted here, for compositional dualization, is the coupling operator surjectivity, property that expresses in a general operator sense the Ladysenskaja-Babulka-Brezzi inf-sup condition. Variational macro-hybridization is performed under the assumption of decomposable primal and dual spaces relative to nonoverlapping domain decompositions. Then, through compositional dualization macro-hybrid mixed problems are obtained, with internal boundary dual traces as Lagrange multipliers. Also, ＂mass＂ preconditioned aug- mentation of three-field formulations are derived, stabilizing macro-hybrid mixed finite element schemes and rendering possible speed up of rates of convergence. Dual mixed incompressible Darcy flow problems illustrate the theory throughout the paper.
