In this study,wc investigatc thc well-posedness of a backward stochastic differential equation with jumps and a central value reflection constraint.The reflection condition is imposed on the real-valued function obtai...In this study,wc investigatc thc well-posedness of a backward stochastic differential equation with jumps and a central value reflection constraint.The reflection condition is imposed on the real-valued function obtained by solving the equation E(arctan(Y_(t)-χ))=0 at each time t∈[0,T].The driver depends on the distribution of the solution process Y and follows a general quadratic-exponential structure.The terminal value is assumed to be bounded.Using a fixed-point argument and Bounded Mean Oscillation(BMO in short)martingale theory,we establish thc cxistence and uniqueness of local solutions,which arc thcn cxtended to construct a global solution over the entire time interval[0,T].展开更多
A new method to solve the boundary value problem arising in the study of scattering of two-dimensional surface water waves by a discontinuity in the surface boundary conditions is presented in this paper. The disconti...A new method to solve the boundary value problem arising in the study of scattering of two-dimensional surface water waves by a discontinuity in the surface boundary conditions is presented in this paper. The discontinuity arises due to the floating of two semi-infinite inertial surfaces of different surface densities. Applying Green＇s second identity to the potential functions and appropriate Green＇s functions, this problem is reduced to solving two coupled Fredholm integral equations with regular kernels. The solutions to these integral equations are used to determine the reflection and the transmission coefficients. The results for the reflection coefficient are presented graphically and are compared to those obtained earlier using other research methods. It is observed from the graphs that the results computed from the present analysis match exactly with the previous results.展开更多
文摘In this study,wc investigatc thc well-posedness of a backward stochastic differential equation with jumps and a central value reflection constraint.The reflection condition is imposed on the real-valued function obtained by solving the equation E(arctan(Y_(t)-χ))=0 at each time t∈[0,T].The driver depends on the distribution of the solution process Y and follows a general quadratic-exponential structure.The terminal value is assumed to be bounded.Using a fixed-point argument and Bounded Mean Oscillation(BMO in short)martingale theory,we establish thc cxistence and uniqueness of local solutions,which arc thcn cxtended to construct a global solution over the entire time interval[0,T].
基金Partially Supported by a DST Research Project to RG(No.SR/FTP/MS-020/2010)
文摘A new method to solve the boundary value problem arising in the study of scattering of two-dimensional surface water waves by a discontinuity in the surface boundary conditions is presented in this paper. The discontinuity arises due to the floating of two semi-infinite inertial surfaces of different surface densities. Applying Green＇s second identity to the potential functions and appropriate Green＇s functions, this problem is reduced to solving two coupled Fredholm integral equations with regular kernels. The solutions to these integral equations are used to determine the reflection and the transmission coefficients. The results for the reflection coefficient are presented graphically and are compared to those obtained earlier using other research methods. It is observed from the graphs that the results computed from the present analysis match exactly with the previous results.
