Stochastics, Control and Robotics

This book discusses various problems in stochastic Processes, Control Theory, Electromagnetics, Classical and Quantum Field Theory & Quantum Stochastics. The problems are chosen to motivate the interested reader to learn more about these subjects from other standard sources. Stochastic Process theory is applied to the study of differential equations of mechanics subject to external noise. Some issues in general relativity like Geodesic motion, field theory in curved space time etc. are discussed via isolated problems. The more recent quantum stochastic process theory as formulated by R.L. Hudson and K. R. Parathasarathy is discussed. This provides a non commutative operator theoretic version of stochastic process theory. V.P. Belavkin's approach to quantum filtering based on non demolition measurements and Hudson Parathasarathy calculus has been discussed in detail. Quantum versions of the simple exclusion model in Markov process theory have been included. 3D Robots carring a current density interacting with an external Klein- Gordon or Electromagnetic field has been given some attention. The readers will after going through this book, be ready to carry out independent research in classical and quantum field theory and stochastic processes as applied to practical problems.