This book introduces essential concepts in stochastic processes that interface seamlessly with applications of interest in science and engineering.

Targeted at graduate students, researchers and practitioners in the field of science and engineering, this book gives a self-contained introduction to a measure-theoretic framework in laying out the definitions and basic concepts of random variables and stochastic diffusion processes. It then continues to weave into a framework of several practical tools and applications involving stochastic dynamical systems. These include tools for the numerical integration of such dynamical systems, nonlinear stochastic filtering and generalized Bayesian update theories for solving inverse problems and a new stochastic search technique for treating a broad class of non-convex optimization problems. MATLAB® codes for all the applications are uploaded on the companion website.

This volume is a collection of research works to honor the late Professor Mark H.A. Davis, whose pioneering work in the areas of Stochastic Processes, Filtering, and Stochastic Optimization spans more than five decades. Invited authors include his dissertation advisor, past collaborators, colleagues, mentees, and graduate students of Professor Davis, as well as scholars who have worked in the above areas. Their contributions may expand upon topics in piecewise deterministic processes, pathwise stochastic calculus, martingale methods in stochastic optimization, filtering, mean-field games, time-inconsistency, as well as impulse, singular, risk-sensitive and robust stochastic control.

This comprehensive textbook covers both classical and geometric aspects of optimization using methods, deterministic and stochastic, in a single volume and in a language accessible to non-mathematicians. It will help serve as an ideal study material for senior undergraduate and graduate students in the fields of civil, mechanical, aerospace, electrical, electronics, and communication engineering. The book includes: Derivative-based Methods of Optimization. Direct Search Methods of Optimization. Basics of Riemannian Differential Geometry. Geometric Methods of Optimization using Riemannian Langevin Dynamics. Stochastic Analysis on Manifolds and Geometric Optimization Methods. This textbook comprehensively treats both classical and geometric optimization methods, including deterministic and stochastic (Monte Carlo) schemes. It offers an extensive coverage of important topics including derivative-based methods, penalty function methods, method of gradient projection, evolutionary methods, geometric search using Riemannian Langevin dynamics and stochastic dynamics on manifolds. The textbook is accompanied by online resources including MATLAB codes which are uploaded on our website. The textbook is primarily written for senior undergraduate and graduate students in all applied science and engineering disciplines and can be used as a main or supplementary text for courses on classical and geometric optimization.

This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.