Elements of Stochastic Methods

This book provides a compact practical exposition of the stochastic methods and their applications for a wide range of fields, including population dynamics, infectious diseases, financial modeling, hydrology, physics, quantum optics, chemistry, and many others. The aim is to give practitioners an idea of how to formulate their current problem stochastically, and how to get an idea of what the predictions of such modeling are. Elements of Stochastic Methods features:

• A treatment based on Markov processes, including an outline of their theoretical foundations, and a description of basic algorithms for simulating Markov processes
• A straightforward and practical formulation of stochastic differential equations and Ito calculus, including simulation methods

Heavy-tailed processes, Mandelbrot's fractional Brownian motion, as well as the more traditional diffusion and jump processes
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This book is an essential resource for researchers, professionals, and graduate students in physics and in any field where random processes are relevant.