The last! This volume closes the Séminaire de Probabilités, a long and rich series that started in 1966 under the name Séminaire de Probabilités de Strasbourg. In addition to a tribute to our colleague Dominique Lépingle, who passed away in December 2021, it presents a selection of texts that reflect recent research streams in probability, including material on random matrices, rough analysis, Markov processes, and subordinators. The featured contributors are J. Bacckhoff, Q. Berger, L. Betencourt, E. Bodiot, A. Bonami, A. Cox, S. Dallaporta, M. Defosseux, F. Delarue, N. Demni, M. Février, A. Grass, B. Hass, M. Huesmann, L. I. Hernandez Ruíz, E. Kahn, L. Miclo, W. Salkeld, and M. Zani.

Includes a tribute to Dominique Lépingle Discusses state-of-the-art research in probability Introduces the use of the theory of rough paths to solve mean-field rough equations

Klappentext

• Part I: In Memoriam Dominique Lépingle.- 1. From Martingales to Multivalued Stochastic Differential Equations in Polyhedral Domains: A Tribute to Dominique Lépingle. - Part II: Regular Contributions.- 2. An Example Driven Introduction to Probabilistic Rough Paths.- 3. Fluctuations of Linear Spectral Statistics of Deformed Wigner Matrices.- 4. Brownian Paths in an Affine Weyl Chamber and Littelmann Paths: What is known and What ought to be.- 5. Strong Solutions to Beta-Jacobi Processes.- 6. On the Helmholtz Decomposition for Finite Markov Processes.- 7. One-Dimensional Discrete Gaussian Markov Processes: Harmonic Decomposition of Invariant Boundary Conditions.- 8. Switching Identities by Probabilistic Means.- 9. An Application of Sparre Andersen’s Fluctuation Theorem for Exchangeable and Sign-Invariant Random Variables.- 10. Precise Asymptotics for the Density and the Upper Tail of Exponential Functionals of Subordinators.- 11. Results for Convergence Rates Associated with Renewal Processes.

  Inhalt

• Part I: In Memoriam Dominique Lépingle .- 1. From Martingales to Multivalued Stochastic Differential Equations in Polyhedral Domains: A Tribute to Dominique Lépingle. - Part II: Regular Contributions. - 2. An Example Driven Introduction to Probabilistic Rough Paths.- 3. Fluctuations of Linear Spectral Statistics of Deformed Wigner Matrices.- 4. Brownian Paths in an Affine Weyl Chamber and Littelmann Paths: What is known and What ought to be.- 5. Strong Solutions to Beta-Jacobi Processes.- 6. On the Helmholtz Decomposition for Finite Markov Processes.- 7. One-Dimensional Discrete Gaussian Markov Processes: Harmonic Decomposition of Invariant Boundary Conditions.- 8. Switching Identities by Probabilistic Means.- 9. An Application of Sparre Andersen's Fluctuation Theorem for Exchangeable and Sign-Invariant Random Variables.- 10. Precise Asymptotics for the Density and the Upper Tail of Exponential Functionals of Subordinators.- 11. Results for Convergence Rates Associated with Renewal Processes.