Error Calculus for Finance and Physics: The Language of Dirichlet Forms (Hardcover, Reprint XXXX)

Intuitive introduction to error structures · Error magnitude · Description of small errors by their biases and variances · Intuitive notion of error structure · How to proceed with an error calculation · Application: Partial integration for a Markov chain · Appendix. Historical comment: The benefit of randomizing physical or natural quantities · Bibliography for Chapter I Strongly-continuous semigroups and Dirichlet forms · Strongly-continuous contraction semigroups on a Banach space · The Ornstein-Uhlenbeck semigroup on R and the associated Dirichlet form · Appendix. Determination of D for the Ornstein-Uhlenbeck semigroup · Bibliography for Chapter II Error structures · Main definition and initial examples · Performing calculations in error structures · Lipschitz functional calculus and existence of densities · Closability of pre-structures and other examples · Bibliography for Chapter III Images and products of error structures · Images · Finite products · Infinite products · Appendix. Comments on projective limits · Bibliography for Chapter IV Sensitivity analysis and error calculus · Simple examples and comments · The gradient and the sharp · Integration by parts formulae · Sensitivity of the solution of an ODE to a functional coefficient · Substructures and projections · Bibliography for Chapter V Error structures on fundamental spaces · Error structures on the Monte Carlo space · Error structures on the Wiener space · Error structures on the Poisson space · Bibliography for Chapter VI Application to financial models · Instantaneous error structure of a financial asset · From an instantaneous error structure to a pricing model · Error calculations on the Black-Scholes model · Error calculations for a diffusion model · Bibliography for Chapter VII Applications in the field of physics · Drawing an ellipse (exercise) · Repeated samples: Discussion · Calculation of lengths using the Cauchy-Favard method (exercise) · Temperature equilibrium of a homogeneous solid (exercise) · Nonlinear oscillator subject to thermal interaction: The Gruneisen parameter · Natural error structures on dynamic systems · Bibliography for Chapter VIII