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Estas notas de aula apresentam uma introdução ampla e progressiva à probabilidade e à simulação estocástica, combinando fundamentos teóricos e aspectos computacionais. O texto inicia com os axiomas da probabilidade, variáveis aleatórias, teoremas assintóticos e desigualdades de concentração, e segue com uma discussão detalhada sobre geração de variáveis discretas e contínuas por diferentes métodos (inversão, rejeição e transformações). São exploradas técnicas de Monte Carlo, intervalos de confiança, e métodos de redução de variância, incluindo variáveis de controle e amostragem por importância, conectadas a desigualdades como a de Chernoff e Hoeffding.

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Os capítulos finais abordam tópicos modernos e aplicados, como cadeias de Markov, métodos de Monte Carlo via MCMC (Metropolis–Hastings e Gibbs), processos de difusão e equações de Fokker–Planck, amostragem de Langevin e Denoising Score Matching para modelagem generativa. O material também inclui uma introdução ao bootstrap sob perspectivas teórica e prática, e encerra com técnicas para otimização e paralelização de códigos em Python.

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Essas notas foram escritas com o objetivo de fornecer uma base sólida para estudantes e pesquisadores interessados em simulação, inferência estatística e aprendizado de máquinas.

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