Séminaire de Probabilités XLII

The tradition of specialized courses in the Séminaires de Probabilités is continued with A. Lejay's Another introduction to rough paths. Other topics from this 42nd volume range from the interface between analysis and probability to special processes, Lévy processes and Lévy systems, branching, penalization, representation of Gaussian processes, filtrations and quantum probability.

Klappentext

This book offers an introduction to rough paths. Coverage also includes the interface between analysis and probability to special processes, Lévy processes and Lévy systems, representation of Gaussian processes, filtrations and quantum probability.

Inhalt

Yet another introduction to rough paths.- Monotonicity of the extremal functions for one-dimensional inequalities of logarithmic Sobolev type.- Non-monotone convergence in the quadratic Wasserstein distance.- On the equation = #x002A;.- Shabat polynomials and harmonic measure.- Radial Dunkl Processes Associated with Dihedral Systems.- Matrix Valued Brownian Motion and a Paper by P#x00F3;lya.- On the Laws of First Hitting Times of Points for One-Dimensional Symmetric Stable L#x00E9;vy Processes.- L#x00E9;vy Systems and Time Changes.- Self-Similar Branching Markov Chains.- A Spine Approach to Branching Diffusions with Applications to L-Convergence of Martingales.- Penalisation of the Standard Random Walk by a Function of the One-Sided Maximum, of the Local Time, or of the Duration of the Excursions.- Canonical Representation for Gaussian Processes.- Recognising Whether a Filtration is Brownian: a Case Study.- Markovian properties of the spin-boson model.- Statistical properties of Pauli matrices going through noisy channels.- Erratum to: New methods in the arbitrage theory of financial markets with transaction costs, in Seminaire XLI.