Long unknown in the West, The Biosphere established the field of biogeochemistry and is one of the classic founding documents of what later became known as Gaia theory. It is the first sustained expression of the idea that life is a geological force that can change Earth's landforms, its climate, and even the contents of its atmosphere. A complete, unabridged translation has never before been available in English. This edition - complete with extensive annotations, an intr...

Stochastic Differential Equations and Diffusion Processes

This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applic...

This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems.While Approximation Me...

Fundamentals of Applied Reservoir Engineering introduces early career reservoir engineers and those in other oil and gas disciplines to the fundamentals of reservoir engineering. Given that modern reservoir engineering is largely centered on numerical computer simulation and that reservoir engineers in the industry will likely spend much of their professional career building and running such simulators, the book aims to encourage the use of simulated models in an appropriate way and exerci...

This book provides a comprehensive and unified introduction to stochastic differential equations and related optimal control problems. The material is new and the presentation is reader-friendly. A major contribution of the book is the development of generalized Malliavin calculus in the framework of white noise analysis, based on chaos expansion representation of stochastic processes and its application for solving several classes of stochastic differential equations with singular data in...

Bacterial Biogeochemistry, Third Edition focuses on bacterial metabolism and its relevance to the environment, including the decomposition of soil, food chains, nitrogen fixation, assimilation and reduction of carbon nitrogen and sulfur, and microbial symbiosis. The scope of the new edition has broadened to provide a historical perspective, and covers in greater depth topics such as bioenergetic processes, characteristics of microbial communities, spatial heterogeneity, transport mechanism...

This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers tempora...

These lecture notes provide an introduction to the applications of Brownian motion to analysis and more generally, connections between Brownian motion and analysis. Brownian motion is a well-suited model for a wide range of real random phenomena, from chaotic oscillations of microscopic objects, such as flower pollen in water, to stock market fluctuations. It is also a purely abstract mathematical tool which can be used to prove theorems in "deterministic" fields of mathematics.The...

In this book the author presents a self-contained account of Harnack inequalities and applications for the semigroup of solutions to stochastic partial and delayed differential equations. Since the semigroup refers to Fokker-Planck equations on infinite-dimensional spaces, the Harnack inequalities the author investigates are dimension-free. This is an essentially different point from the above mentioned classical Harnack inequalities. Moreover, the main tool in the study is a new coupling ...

Petroleum Rock Mechanics: Drilling Operations and Well Design covers the fundamentals of solid mechanics and petroleum rock mechanics and their application to oil and gas-related drilling operations and well design. More specifically, it examines the role of formation, strength of rock materials, and wellbore mechanics, along with the impact of in-situ stress changes on wellbore and borehole behavior. Practical examples with solutions and a comprehensive glossary of terminologies are provi...

This book is divided into two parts, the first of which seeks to connect the phase transitions of various disciplines, including game theory, and to explore the synergies between statistical physics and combinatorics. Phase Transitions has been an active multidisciplinary field of research, bringing together physicists, computer scientists and mathematicians. The main research theme explores how atomic agents that act locally and microscopically lead to discontinuous macroscopic changes. A...