Construction of noncanonical representations of a Brownian motion
Construction of noncanonical representations of a Brownian motion
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布朗运动的非规范表示的构造
DOI：
10.32917/hmj/1206126962
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发表时间：
1997
影响因子：
0.2
通讯作者：
Hiroshi Muraoka
中科院分区：
文献类型：
--
作者：
Y. Hibino;M. Hitsuda;Hiroshi Muraoka
抽象的。设布朗运动B = {B（t）; t ∈ [0，1]}.对于任意线性无关系统g = {g1，g2，. . .，gN}，构造了关于B的非正则布朗运动B g = {B g（t）; t ∈ [0，1]}.具体地，Ht（B）在Ht（B）中的正交补是{Δ t 0 g1（u）dB（u），Δ t 0 g2（u）dB（u），. . .，<0 gN（u）dB（u）}。作为一个特殊情况下，莱维的例子，非正则表示的布朗运动。对于B图的构造，我们使用了部分等距的理论。得到了一个推广的哈代不等式，并将其作为一个重要引理加以应用.
Abstract. Give a Brownian motion B = {B(t); t ∈ [0, 1]}. For any linearly independent system g = {g1, g2, . . . , gN} in L[0, 1], we construct a Brownian motion B̄g = {B̄g(t); t ∈ [0, 1]} which is noncanonical with respect to B. In detail, the orthogonal complement of Ht(B̄g) in Ht(B) is the linear span of {∫ t 0 g1(u)dB(u), ∫ t 0 g2(u)dB(u), . . . , ∫ t 0 gN (u)dB(u)}. As a special case, Lévy’s examples of noncanonical representations of a Brownian motion are included. For the construction of B̄g, we use the theory of a partial isometry. A generalized Hardy inequality is derived and applied as an important lemma.