From Classical to Modern Probability

InhaltsangabeAsymptotic of the Heat Kernel in Unbounded Domains.- 1 Introduction.- 2 Ratio theorem for domains with harmonic cone C? of dimension 1.- 3 Benedicks domains.- References.- Spin Systems with Long Range Interactions.- 1 Ising spin systems.- 2 Phase transition.- 3 Time evolution.- References.- Nonlinear Dirichlet Problem and Nonlinear Integration.- 1 Generalities.- 2 Preliminaries on capacities.- 3 Radon capacities.- 4 Lusin capacities.- 5 Answering the questions and last words.- References.- First-Passage Percolation.- 1 The basic model and the shape model.- 2 Exponential bounds for large deviations.- 3 Bounds of moderate deviations.- References.- Central Limit Theorem for Markov Processes.- 1 Introduction.- 2 A warming-up example.- 3 Central limit theorem for Markov processs.- 4 Regularity of the diffusion coefficient.- References.- Stochastic Orders and Stopping Times in Brownian Motion.- 1 Introduction.- 2 Martingales and stochastic orders.- 3 Skorohod embeddings in standard Brownian motion.- 4 A maximal property of Azéma-Yor stopped Brownian motion.- 5 Practical description of the optimal stopping time for the look-back American put option problem.- References.