The existence and uniqueness of the solution of an integral equation driven by a p-semimartingale of special type
The existence and uniqueness of the solution of an integral equation driven by a p-semimartingale of special type
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DOI：
10.1016/s0304-4149(01)00145-4
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发表时间：
2002-04
影响因子：
1.4
通讯作者：
K. Kubilius
中科院分区：
文献类型：
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作者：
K. Kubilius
我们考虑由标准布朗运动和分数布朗运动驱动的积分方程。由于fBm不是半鞅，我们不能用半鞅理论来定义关于fBm的积分。在q有界变差的连续函数空间（q>2）中，得到了解的存在唯一性条件。
We consider the integral equation driven by a standard Brownian motion and fractional Brownian motion (fBm). Since fBm is not a semimartingale, we cannot use the semimartingale theory to define an integral with respect to the fBm. Furthermore, a well-developed theory of stochastic differential equations is not applicable to solve it. Existence and uniqueness conditions are obtained for a solution in the space of continuous functions with q-bounded variation, q>2.