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Stochastic Partial Differential Equations with Lévy Noise
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  • Cited by 119
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Lv, Huibin Liu, Zhijun Li, Zuxiong Wang, Lianwen and Xu, Dashun 2018. Two impulsive stochastic delay single-species models incorporating Lévy noise. Journal of Applied Mathematics and Computing,

    Li, Zhi Yan, Litan and Xu, Liping 2018. Stepanov-like almost automorphic solutions for stochastic differential equations with Lévy noise. Communications in Statistics - Theory and Methods, Vol. 47, Issue. 6, p. 1350.

    Benth, Fred Espen and Simonsen, Iben Cathrine 2018. The Heston Stochastic Volatility Model in Hilbert Space. Stochastic Analysis and Applications, p. 1.

    Su, Xiaoyan and Li, Miao 2018. The regularity of fractional stochastic evolution equations in Hilbert space. Stochastic Analysis and Applications, p. 1.

    Lin, Lin and Gao, Hongjun 2018. A Stochastic Generalized Ginzburg–Landau Equation Driven by Jump Noise. Journal of Theoretical Probability,

    Criens, David 2018. Cylindrical Martingale Problems Associated with Lévy Generators. Journal of Theoretical Probability,

    Cyr, Justin Tang, Sisi and Temam, Roger 2018. Trends in Applications of Mathematics to Mechanics. Vol. 27, Issue. , p. 289.

    Huan, Diem Dang and Agarwal, Ravi P. 2018. Asymptotic behavior, attracting and quasi-invariant sets for impulsive neutral SPFDE driven by Lévy noise. Stochastics and Dynamics, Vol. 18, Issue. 01, p. 1850010.

    Benth, Fred Espen and Krühner, Paul 2018. Approximation of forward curve models in commodity markets with arbitrage-free finite-dimensional models. Finance and Stochastics, Vol. 22, Issue. 2, p. 327.

    Frey, Rüdiger Rösler, Lars and Lu, Dan 2018. Corporate security prices in structural credit risk models with incomplete information. Mathematical Finance,

    Yang, Desheng 2018. Pathwise uniqueness for stochastic evolution equations with Hölder drift and stable Lévy noise. Nonlinear Differential Equations and Applications NoDEA, Vol. 25, Issue. 3,

    Guo, Rong and Pei, Bin 2018. Stochastic Averaging Principles for Multi-Valued Stochastic Differential Equations Driven by Poisson Point Processes. Stochastic Analysis and Applications, p. 1.

    Koley, Ujjwal Majee, Ananta K and Vallet, Guy 2018. A finite difference scheme for conservation laws driven by Lévy noise. IMA Journal of Numerical Analysis, Vol. 38, Issue. 2, p. 998.

    Sun, Kai and Wang, Yan 2017. Almost automorphic solutions for stochastic differential equations driven by Lévy noise with exponential dichotomy. Stochastic Analysis and Applications, Vol. 35, Issue. 2, p. 211.

    Li, Kexue Peng, Jigen and Jia, Junxiong 2017. Explosive solutions of parabolic stochastic partial differential equations with Lévy noise. Discrete and Continuous Dynamical Systems, Vol. 37, Issue. 10, p. 5105.

    Xu, Jie 2017. L p -strong convergence of the averaging principle for slow–fast SPDEs with jumps. Journal of Mathematical Analysis and Applications, Vol. 445, Issue. 1, p. 342.

    Lang, Annika Petersson, Andreas and Thalhammer, Andreas 2017. Mean-square stability analysis of approximations of stochastic differential equations in infinite dimensions. BIT Numerical Mathematics, Vol. 57, Issue. 4, p. 963.

    Cordoni, F. Di Persio, L. and Oliva, I. 2017. A nonlinear Kolmogorov equation for stochastic functional delay differential equations with jumps. Nonlinear Differential Equations and Applications NoDEA, Vol. 24, Issue. 2,

    Desch, G. and Londen, S.-O. 2017. Regularity of stochastic integral equations driven by Poisson random measures. Journal of Evolution Equations, Vol. 17, Issue. 1, p. 263.

    Högele, Michael A. and da Costa, Paulo Henrique 2017. Strong Averaging Along Foliated Lévy Diffusions with Heavy Tails on Compact Leaves. Potential Analysis, Vol. 47, Issue. 3, p. 277.


Book description

Recent years have seen an explosion of interest in stochastic partial differential equations where the driving noise is discontinuous. In this comprehensive monograph, two leading experts detail the evolution equation approach to their solution. Most of the results appeared here for the first time in book form. The authors start with a detailed analysis of Lévy processes in infinite dimensions and their reproducing kernel Hilbert spaces; cylindrical Lévy processes are constructed in terms of Poisson random measures; stochastic integrals are introduced. Stochastic parabolic and hyperbolic equations on domains of arbitrary dimensions are studied, and applications to statistical and fluid mechanics and to finance are also investigated. Ideal for researchers and graduate students in stochastic processes and partial differential equations, this self-contained text will also interest those working on stochastic modeling in finance, statistical physics and environmental science.


'Summarising, this book is an excellent addition to the literature on stochastic partial differential equations in general and in particular with respect to evolution equations driven by a discontinuous noise. The exposition is self-contained and very well written and, in my opinion, will become a standard tool for everyone working on stochastic evolution equations and related areas.'

Source: Zentralblatt MATH

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