Stochastic Partial Differential Equations and Related Fields (eBook)

Preface.- Longer Contributions: V. Bogachev, Stationary Fokker-Planck-Kolmogorov equations.- M. Fukushima, Liouville property of harmonic functions of finite energy for Dirichlet forms.- B. Gess, Regularization and well-posedness by noise for ordinary and partial differential equations.- M. Gubinelli, N. Perkowski, An introduction to singular SPDEs.-  N. Perkowski, M. Gubinelli, Probabilistic approach to the stochastic Burgers equation.- G. Da Prato, Fokker-Planck equations in Hilbert spaces.- Stochastic Partial Differential Equations and Regularity structures: Z. Brzezniak, G. Dhariwal, J. Hussain, M. Mariani, Stochastic and deterministic constrained partial differential equations.- P. Coupek, B. Maslowski, J. Šnupárková, SPDEs with Volterra Noise.- R. Dalang, Hitting probabilities for systems of stochastic PDEs: an overview.- C. Denis, T. Funaki, S. Yokoyama, Curvature motion perturbed by a direction-dependent colored noise.- N.  Krylov, E. Priola, Poisson stochastic process and basic Schauder and Sobolev estimates in the theory of parabolic equations.- H. D. Luu, M. J. Garrido-Atienza, B. Schmalfuss, Dynamics of SPDE driven by a small fractional Brownian motion with Hurst parameter larger than ½.- C. Marinelli, L. Scarpa, On the well-posedness of SPDEs with singular drift in divergence form.- L. J. de Naurois, A. Jentzen, T. Welti, Lower bounds for weak approximation errors for spatial spectral Galerkin approximations of stochastic wave equations.- J. M. Tölle, Estimates for nonlinear stochastic partial differential equations with gradient noise via Dirichlet forms.- W. Yan, J. Duan, Random data Cauchy problem for some dispersive equations.- Lorenzo Zambotti, SPDEs and Renormalisation.- D. Zhang, Recent progress on stochastic nonlinear Schrödinger equations.- Stochastic Analysis including geometric aspects: V. Barbu, Generalized Solutions to Nonlinear Fokker-Planck Equations with Linear Drift.- Y. Bruned, I. Chevyrev, P. Friz, Examples of Renormalized SDEs.- K.D. Elworthy, Generalised Weitzenböck formulae for differential operators in Hörmander form.- M. Hofmanova, On the Rough Gronwall Lemma and its Applications.- X.-M. Li, Doubly Damped Stochastic Parallel translations and Hessian formulas.- M. Scheutzow, I. Vorkastner, Synchronization, Lyapunov exponents and stable manifolds for random dynamical Systems.- S. Shaposhnikov, Nonlinear Fokker-Planck-Kolmogorov equations for measures.- F.-Y. Wang, Coupling by Change of Measure, Harnack Inequality and Hypercontractivity.- X. Zhang, Multidimensional Singular Stochastic Differential Equations.- Dirichlet forms, Markov Processes and Potential theory: L. Beznea, I. Cimpean, L. Beznea, I. Cimpean. Invariant, super and quasi-martingale functions of a Markov process.- Z.-Q. Chen, T.  Kumagai, J. Wang, Mean value inequalities for jump processes.- X. Chen, Z.-M. Ma, X. Peng, Positivity preserving semigroups and positivity preserving coercive forms.- N. Jacob, J. Harris, Some Thoughts and Investigations on Densities of One-Parameter Operator Semi-groups.- H. Kawabi, Strong uniqueness of Dirichlet operators related to stochastic quantization under exponential interactions in one-dimensional infinite volume.- V. Knopova, R. Schilling, A Probabilistic proof of the breakdown of Besov regularity in L-shaped domains.- T. Masayoshi, Symmetric Markov Processes with Tightness Property.- Applications including Mathematical Physics: J. Chen, M. Hinz, A. Teplyaev, From non-symmetric particle systems to non-linear PDEs on fractals.- Y. Kozitsky, Equilibrium States, Phase Transitions and Dynamics in Quantum Anharmonic Crystals.- X. Liu, B. Zegarlinski, On Continuous Coding.- H. Osada, Infinite-dimensional Stochastic Differential Equations with Symmetry.- R. Zhu, X. Zhu, Recent progress on the Dirichlet forms associated with stochastic quantization Problems.