In this paper,we first investigate some basic properties of asymptotically mean almost periodic random sequences on Z + and then show some properties of asymptotically mean almost periodic solutions to random differen...In this paper,we first investigate some basic properties of asymptotically mean almost periodic random sequences on Z + and then show some properties of asymptotically mean almost periodic solutions to random difference equations.展开更多
We consider the random difference equations S =_d(X + S)Y and T =_dX + TY, where =_ddenotes equality in distribution, X and Y are two nonnegative random variables, and S and T on the right hand side are independent of...We consider the random difference equations S =_d(X + S)Y and T =_dX + TY, where =_ddenotes equality in distribution, X and Y are two nonnegative random variables, and S and T on the right hand side are independent of(X, Y). Under the assumptions that X follows a subexponential distribution with a nonzero lower Karamata index, that Y takes values in [0, 1] and is not degenerate at 0 or 1, and that(X, Y) fulfills a certain dependence structure via the conditional tail probability of X given Y, we derive some asymptotic formulas for the tail probabilities of the weak solutions S and T to these equations. In doing so we also obtain some by products which are interesting in their own right.展开更多
基金Supported by the NNSF of China(No.11171191)the NSF of Shandong Province(No.ZR2010AL011)
文摘In this paper,we first investigate some basic properties of asymptotically mean almost periodic random sequences on Z + and then show some properties of asymptotically mean almost periodic solutions to random difference equations.
基金supported by the National Science Foundation of the United States (Grant No. CMMI-1435864)
文摘We consider the random difference equations S =_d(X + S)Y and T =_dX + TY, where =_ddenotes equality in distribution, X and Y are two nonnegative random variables, and S and T on the right hand side are independent of(X, Y). Under the assumptions that X follows a subexponential distribution with a nonzero lower Karamata index, that Y takes values in [0, 1] and is not degenerate at 0 or 1, and that(X, Y) fulfills a certain dependence structure via the conditional tail probability of X given Y, we derive some asymptotic formulas for the tail probabilities of the weak solutions S and T to these equations. In doing so we also obtain some by products which are interesting in their own right.
