Random integral equations with applications to life sciences and engineering

Description

Because probability and statistics are as much about intuition and problem solving, as they are about theorem proving, students can find it very difficult to make a successful transition from lectures to examinations and practice. Since the subject is critical in many modern applications, Yuri Suhov and Michael Kelbert have rectified deficiencies in traditional lecture-based methods, by combining a wealth of exercises for which they have supplied complete solutions. These solutions are adapted to needs and skills of students and include basic mathematical facts as needed In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat.  Read more... Front Cover; Random Integral Equations With Applications to Life Sciences and Engineering; Copyright Page; Contents; Preface; General Introduction; Chapter I. Preliminaries and Formulation of the Stochastic Equations; Chapter II. Some Random Integral Equations of the Volterra Type with Applications; Chapter III. Approximate Solution of the Random Volterra Integral Equation and an Application to Population Growth Modeling; Chapter IV. A Stochastic Integral Equation of the Fredholm Type and Some Applications; Chapter V. Random Discrete Fredholm and Volterra Systems. Chapter VI. Nonlinear Perturbed Random Integral Equations and Application to Biological SystemsChapter VII. On a Nonlinear Random Integral Equation with Application to Stochastic Chemical Kinetics; Chapter VIII. Stochastic Integral Equations of the Ito Type; Chapter IX. Stochastic Nonlinear Differential Systems; Chapter X. Stochastic Integrodifferential Systems; Bibliography; Index