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60J65 Probability theory and stochastic processes -- Markov processes -- Brownian motion

60G07 Probability theory and stochastic processes -- Stochastic processes -- General theory of processes

60H15 Probability theory and stochastic processes -- Stochastic analysis -- Stochastic partial differential equations

35K86 Partial differential equations -- Parabolic equations and systems -- Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities En-ligne: Springerlink - résumé | zbMath | MSN

Location | Call Number | Status | Date Due |
---|---|---|---|

Salle S | 12439-01 / Ecole STF (Browse Shelf) | Available |

Ecole STFBrownian motion and its applications to mathematical analysis | Ecole STFRandom walks on disordered media and their scaling limits | Ecole STFBranching random walks | Ecole STFRandom obstacle problems | Ecole STFLarge deviations for random graphs | Ecole STFEstimation and testing under sparsity |

Bibliogr. p. 159-162

Publisher’s description: Studying the fine properties of solutions to Stochastic (Partial) Differential Equations with reflection at a boundary, this book begins with a discussion of classical one-dimensional diffusions as the reflecting Brownian motion, devoting a chapter to Bessel processes, and moves on to function-valued solutions to SPDEs. Inspired by the classical stochastic calculus for diffusions, which is unfortunately still unavailable in infinite dimensions, it uses integration by parts formulae on convex sets of paths in order to describe the behaviour of the solutions at the boundary and the contact set between the solution and the obstacle. The text may serve as an introduction to space-time white noise, SPDEs and monotone gradient systems. Numerous open research problems in both classical and new topics are proposed.

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