We consider the necessary conditions for backward doubly stochastic control system, via the second-order Taylor expansion we have obtained. All the results are got under no restriction on the convexity of control domain and the diffusion coefficient does not contain the control variable.

In recent years methods of data analysis for point processes have received some attention, for example, by Cox & Lewis (1966) and Lewis (1964). In particular Bartlett (1963a, b) has introduced methods of analysis based on the point spectrum. Theoretical models are relatively sparse. In this paper the theoretical properties of a class of processes with particular reference to the point spectrum ...

In [l] R. Sinkhorn proved the following theorem: Let A be a positive square matrix. Then there exist two diagonal matrices D, , D, whose diagonal elements are positive such that D,AD, is doubly stochastic. Moreover, these matrices are uniquely determkd up to scalar factors. In addition, Sinkhorn gave some examples which show that the theorem fails for some nonnegative matrices A. Marcus and New...

this paper presents an approach for solving a nonlinear stochastic differential equations (nsdes) using a new basis functions (nbfs). these functions and their operational matrices areused for representing matrix form of the nbfs. with using this method in combination with the collocation method, the nsdes are reduced a stochastic nonlinear system of equations and unknowns. then, the error anal...

We study reflected solutions of one-dimensional backward doubly stochastic differential equations (BDSDEs in short). The “reflected” keeps the solution above a given stochastic process. We get the uniqueness and existence by penalization. For the existence of backward stochastic integral, our proof is different from [KKPPQ] slightly. We also obtain a comparison theorem for reflected BDSDEs. At ...