摘要
对两指标Wiener过程产生的完备σ-域族(F_z),z∈R_+~2。证明了如下的定理:若G_n和G是零点的有界停止的邻域。而且G_n↓G,则F_(G_n)↓F_G;若D为零点的有界停止邻域,R_z为矩形[0,z],D∧z=D∩R_z,则域流(F_(D∧Z))满足条件F1—F4;若(M_z)为关于域流(F_z)的局部平方可积鞅,D是使得Wiener过程W的停止,W^D为关于域流(F_(D∧Z))的Wiener过程的零点的有界停止邻域,则M的停止M^D为关于域流(F_(D∧Z))的局部平方可积鞅,从而M^D为(F)局部平方可积鞅。
In this paper following theorems for the complete α-fields(F_z) generated by the two-parameter Wiener process have been proved by authors. If G_n and G are bounded stopping neighborhood of zero point and G_n↓G, then fields F_(Gn)↓F_G. If D is a bounded stopping neighborhood of zero point, R, is a rectangle [0, z], z∈R_+~2, and D∧z=D∩R_2, then fields (F_(D∧Z)) satisfy the conditions F1—F4. If (M_Z) for fields (F_Z) is a local square integrable martingales, is a bounded stopping neighborhood of zero point, such that the stopping W^D of Wiener process W at D is (F_(D∧Z)) Wiener process, then the stopping M^D of M is (F_(D∧Z)) local square integrable martingale, and hence M^D is local square integable (F_Z) martingale.
关键词
两指标域流
正则性
局部鞅停止
不变性
two-parameter Wiener process, bounded stopping neighborhood of zero point, local square integrable martingales, stopping of process
