论文标题
在希尔伯特空间中的随机整合相对于圆柱状的马丁加尔评估措施
Stochastic integration in Hilbert spaces with respect to cylindrical martingale-valued measures
论文作者
论文摘要
在这项工作中，我们介绍了有关运算符值集成的随机整合理论，相对于希尔伯特空间中的某些类别的圆柱形马丁加尔市值措施。该积分是通过Hilbert-Schmidt操作员定理构造的，并统一了希尔伯特空间中随机整合的其他几种理论。特别是，我们的理论涵盖了相对于希尔伯特空间有价值的莱维过程的随机整合理论（不需要满足任何时刻条件），相对于具有（弱）第二矩（弱）第二矩的圆柱lévy过程，并且相对于LévyVyValued估算的随机捕捞量，并进行了有限的第二刻。作为我们整合理论的应用，我们证明了由乘法性圆柱形的Martingale值测量噪声驱动的随机随机部分微分方程的解决方案的存在和独特性，并具有相当一般的系数。
In this work we introduce a theory of stochastic integration for operator-valued integrands with respect to some classes of cylindrical martingale-valued measures in Hilbert spaces. The integral is constructed via the radonification of cylindrical martingales by a Hilbert-Schmidt operator theorem and unifies several other theories of stochastic integration in Hilbert spaces. In particular, our theory covers the theory of stochastic integration with respect to a Hilbert space valued Lévy process (which is not required to satisfy any moment condition), with respect to a cylindrical Lévy processes with (weak) second moments and with respect to a Lévy-valued random martingale measures with finite second moment. As an application of our theory of integration we prove existence and uniqueness of solutions for stochastic stochastic partial differential equations driven by multiplicative cylindrical martingale-valued measure noise with rather general coefficients.
