Séminaire de Probabilités XLI Stochastic processes are as usual the main subject of the Séminaire with contributions on Brownian motion (fractional or other) Lévy processes martingales and probabilistic finance. Other probabilistic themes are also present: large random matrices statistical mechanics. The contributions in this volume provide a sampling of recent results on these topics. All contributions with the exception of two are written in English language. Spectral gap inequality for a colored disordered lattice gas On large deviations for the spectral measure of discrete Coulomb gas Estimates for moments of random matrices with Gaussian elements Geometric interpretation of the cumulants for random matrices previously defined as convolutions on the symmetric group Fluctuations of spectrally negative Markov additive processes On Continuity Properties of the Law of Integrals of Lévy Processes A Law of the Iterated Logarithm for Fractional Brownian Motions A simple theory for the study of SDEs driven by a fractional Brownian motion in dimension one Proof of a Tanaka like formula stated by J. Rosen in Séminaire XXXVIII Une preuve simple d’un résultat de Dufresne Creation or deletion of a drift on a Brownian trajectory Extending Chacon Walsh: Minimality and Generalised Starting Distributions Transformations browniennes et compléments indépendants: résultats et problèmes ouverts Hyperbolic random walks The Hypergroup Property and Representation of Markov Kernels A new look at ‘Markovian’ Wiener Hopf theory Separability and completeness for the Wasserstein distance A probabilistic interpretation to the symmetries of a discrete heat equation On the tail distributions of the supremum and the quadratic variation of a càdlàg local martingale The Burkholder Davis Gundy Inequality for Enhanced Martingales On Martingale Selectors of Cone Valued Processes No asymptotic free lunch reviewed in the light of Orlicz spaces New methods in the arbitrage theory of financial markets with transaction costs.