Applied Stochastic Differential Equations

Simo Särkkä is Associate Professor of Electrical Engineering and Automation at Aalto University, Finland, Technical Advisor at IndoorAtlas Ltd., and Adjunct Professor at Tampere University of Technology and Lappeenranta University of Technology. His research interests are in probabilistic modeling and sensor fusion for location sensing, health technology, and machine learning. He has authored over ninety peer-reviewed scientific articles as well as one book, titled Bayesian Filtering and Smoothing (Cambridge, 2013). Arno Solin is an Academy of Finland Postdoctoral Researcher with Aalto University, Finland and Technical Advisor at IndoorAtlas Ltd. His research interests focus on models and applications in sensor fusion for tracking and navigation, brain imaging, and machine learning problems. He has published over twenty peer-reviewed scientific papers, and has won several hackathons and competitions in mathematical modeling, including the 2014 Schizophrenia classification on Kaggle.

• 1. Introduction; 2. Some background on ordinary differential equations; 3. Pragmatic introduction to stochastic differential equations; 4. Ito calculus and stochastic differential equations; 5. Probability distributions and statistics of SDEs; 6. Statistics of linear stochastic differential equations; 7. Useful theorems and formulas for SDEs; 8. Numerical simulation of SDEs; 9. Approximation of nonlinear SDEs; 10. Filtering and smoothing theory; 11. Parameter estimation in SDE models; 12. Stochastic differential equations in machine learning; 13. Epilogue.

'Stochastic differential equations have long been used by physicists and engineers, especially in filtering and prediction theory, and more recently have found increasing application in the life sciences, finance and an ever-increasing range of fields. The authors provide intended users with an intuitive, readable introduction and overview without going into technical mathematical details from the often-demanding theory of stochastic analysis, yet clearly pointing out the pitfalls that may arise if its distinctive differences are disregarded. A large part of the book deals with underlying ideas and methods, such as analytical, approximative and computational, which are illustrated through many insightful examples. Linear systems, especially with additive noise and Gaussian solutions, are emphasized, though nonlinear systems are not neglected, and a large number of useful results and formulas are given. The latter part of the book provides an up to date survey and comparison of filtering and parameter estimation methods with many representative algorithms, and culminates with their application to machine learning.' Peter Kloeden, Johann Wolfgang Goethe-Universität Frankfurt am Main