An Introduction to Random Currents and Their Applications
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Beschreibung
This book introduces random currents by presenting underlying mathematical methods necessary for applications. The theory of currents is an advanced topic in geometric measure theory that extends distribution to linear functionals within the space of differential forms of any order. Methods to extend random distributions to random currents are introduced and analyzed in this book. Beginning with an overview of mathematical aspects of the theory of currents, this book moves on to examine applications in medicine, material science, and image analysis. Applied researchers will find the practical modern mathematical methods along with the detailed appendix useful to stimulate new applications and research.
Presents mathematical methods necessary for applications in medicine, material science, and image analysis Extends random distributions to random currents Stimulates new applications and research through mathematical methods
Autor*in
Vincenzo Capasso
Themen in »An Introduction to Random Currents and Their Applications«
theory of currents Geometric Measure Theory linear functionals statistical shape analysis Crystal dislocations Tumor-driven angiogenesis Stochastic Geometry Push-forward of a current Operations on currents Boundary, and Lie derivative of a current Gaussian currents in statistical shape analysis Random currents on Hilbert spaces Gaussian currents Elements of measure theory Fundamentals of Stochastic Processes
Stimmen zu »An Introduction to Random Currents and Their Applications«
“The book will be useful to mathematicians and applied scientists.” (Jordan M. Stoyanov, zbMATH 1426.28001, 2020)
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