STOCHASTIC INTEGRAL & DIFFERENTIAL EQUATIONS IN MATH MODEL

The modelling of systems by differential equations usually requires that the parameters involved be completely known. Such models often originate from problems in physics or economics where we have insufficient information on parameter values. One important class of stochastic mathematical models is stochastic partial differential equations (SPDEs), which can be seen as deterministic partial differential equations (PDEs) with finite or infinite dimensional stochastic processes — either with colour noise or white noise. Though white noise is a purely mathematical construction, it can be a good model for rapid random fluctuations.

Stochastic Integral and Differential Equations in Mathematical Modelling concerns the analysis of discrete-time approximations for stochastic differential equations (SDEs) driven by Wiener processes. It also provides a theoretical basis for working with SDEs and stochastic processes.

This book is written in a simple and clear mathematical logical language, with basic definitions and theorems on stochastic calculus provided from the outset. Each chapter contains illustrated examples via figures and tables. The reader can also construct new wavelets by using the procedure presented in the book. Stochastic Integral and Differential Equations in Mathematical Modelling fulfils the existing gap in the literature for a comprehensive account of this subject area.

Contents:

• Preface
• About the Author
• List of Figures
• Index
• Introduction and Preliminaries of Stochastic Calculus
• Analytical Solutions of Stochastic Differential Equations
• Numerical Solutions of Stochastic Integral Equation
• Numerical Solutions of Multidimensional Stochastic Integral Equation
• Numerical Solutions of Stochastic Integral Equations with Fractional Brownian Motion
• Numerical Solutions of Stochastic Differential Equations Arising in Physical Phenomena
• Numerical Solutions of Stochastic Point Kinetics Equations
• Numerical Solutions of Fractional Stochastic Point Kinetics Equation
• Conclusions and Future Directions
• References
• Index

Readership: Useful for Master degree students with numerical methods as a specialization and Research scholars working in this field. Supplementary book for undergraduate students or those in engineering working on wavelets.

Key Features:

• The key selling point of the book is it covers various analytical and numerical methods for solving stochastic differential equations and integral equations
• Suitable for both postgraduate and research students in various branches of engineering/general and applied sciences
• There are very few books available in the open literature which covers the very efficient use of both analytical and numerical methods (especially wavelet methods) for solving stochastic differential equations and integral equations and systems and applications with examples
• Many real physical phenomena are modelled by stochastic differential equations
• Problems involving fractional Brownian motion have also been discussed through examples
• Stochastic point kinetics model has also been solved for various reactivities with detailed graphs and explanations
• It will fill the blank space that a lack of a comprehensive book of stochastic differential equations has created