## Recent Development in Stochastic Dynamics and Stochastic AnalysisStochastic dynamical systems and stochastic analysis are of great interests not only to mathematicians but also scientists in other areas. Stochastic dynamical systems tools for modeling and simulation are highly demanded in investigating complex phenomena in, for example, environmental and geophysical sciences, materials science, life sciences, physical and chemical sciences, finance and economics. The volume reflects an essentially timely and interesting subject and offers reviews on the recent and new developments in stochastic dynamics and stochastic analysis, and also some possible future research directions. Presenting a dozen chapters of survey papers and research by leading experts in the subject, the volume is written with a wide audience in mind ranging from graduate students, junior researchers to professionals of other specializations who are interested in the subject. |

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### Contents

2 Decoherent Information of Quantum Operations Xuelian Cao Nan Li and Shunlong Luo | 23 |

3 Stabilization of Evolution Equations by Noise Tomas Caraballo and Peter E Kloeden | 43 |

4 Stochastic Quantification of Missing Mechanisms in Dynamical Systems Baohua Chen and Jinqiao Duan | 67 |

5 Banach SpaceValued Functionals of White Noise Yin Chen and Caishi Wang | 77 |

6 Hurst Index Estimation for SelfSimilar Processes with LongMemory Alexandra Chronopoulou and Frederi G Viens | 91 |

7 Modeling Colored Noise by Fractional Brownian Motion Jinqiao Duan Chujin Li and Xiangjun Wang | 119 |

8 A Sufficient Condition for NonExplosion for a Class of Stochastic Partial Dierential Equations Hongbo Fu Daomin Cao and Jinqiao Duan | 131 |

9 The Influence of Transaction Costs on Optimal Control for an Insurance Company with a New Value Function Lin He Zongxia Liang and Fei Xing | 143 |

11 Class II SemiSubgroups of the Infinite Dimensional Rotation Group and Associated Lie Algebra Takeyuki Hida and Si Si | 177 |

12 Stopping Weyl Processes Robin L Hudson | 185 |

13 KarhunenLoeve Expansion for Stochastic Convolution of Cylindrical Fractional Brownian Motions Zongxia Liang | 195 |

A Short Survey With New Estimates Ivan Nourdin and Giovanni Peccati | 207 |

15 On Stochastic Integrals with Respect to an Innite Number of Poisson Point Process and Its Applications Guanglin Rang Qing Li and Sheng You | 237 |

16 Levy White Noise Elliptic SPDEs and Euclidean Random Fields JiangLun Wu | 251 |

17 A Short Presentation of Choquet Integral JiaAn Yan | 269 |

10 Limit Theorems for pVariations of Solutions of SDEs Driven by Additive Stable Levy Noise and Model Selection for PaleoClimatic Data Claudia ... | 161 |

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### Common terms and phrases

assume asymptotic boundary conditions bounded Caraballo Choquet integral colored noise comonotonic consider continuous convergence correlations covariance decoherent information defined denote deterministic Dirichlet distribution estimator exists exponentially stable formula fractional Brownian motion Gaussian process Hermite process Hilbert space Hurst parameter implies inequality Infinite Dimensional isonormal Gaussian process Itô Lemma Lévy Lévy processes limit theorems Lipschitz long-memory Malliavin calculus martingale Math Mathematics measure monotone set function multiple Neumann norm Nourdin Nualart parameter H partial differential equations PDEs Peccati Phys Poisson probability problem Proof properties Proposition prove quantum field quantum operation random fields random variables result satisfies scalar self-similarity sequence SPDEs stabilization stationary Stein’s method Stochastic Analysis stochastic calculus stochastic differential equations stochastic integral stochastic process Stratonovich noise Theorem 3.1 theory unique variations vector Wang wavelets white noise Wiener chaos Wiener process Wightman functions Xdfi zero