Explore advanced topics in stochastic dynamics, filtering, and optimization with this comprehensive guide from The Bookish Owl. Ideal for graduate students, scientists, and engineers, this self-contained text offers a measure-theoretic introduction to stochastic processes. Delve into practical applications, including numerical integration of dynamical systems, nonlinear stochastic filtering, and generalized Bayesian updates for inverse problems. Discover innovative stochastic search techniques for non-convex optimization. This essential resource provides a robust foundation for understanding and applying cutting-edge stochastic methods. Companion MATLAB® codes are available online, enhancing practical learning and research. Elevate your expertise in scientific and engineering computation.