Böcker av Nicolas Privault

This text presents selected applications of discrete-time stochastic processes that involve random interactions and algorithms, and revolve around the Markov property. It covers recurrence properties of (excited) random walks, convergence and mixing of Markov chains, distribution modeling using phase-type distributions, applications to search engines and probabilistic automata, and an introduction to the Ising model used in statistical physics. Applications to data science are also considered via hidden Markov models and Markov decision processes. A total of 32 exercises and 17 longer problems are provided with detailed solutions and cover various topics of interest, including statistical learning.

This book presents an introduction to pricing and hedging in discrete and continuous time financial models, emphasizing both analytical and probabilistic methods. It demonstrates both the power and limitations of mathematical models in finance, covering the basics of stochastic calculus for finance.

This book provides an undergraduate introduction to discrete and continuous-time Markov chains and their applications. It includes more than 70 exercises, along with complete solutions, that help illustrate and present all concepts.