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Markov Processes for Stochastic Modeling, 2nd Edition by Oliver Ibe

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10

Diffusion Processes

10.1 Introduction

Diffusion processes are continuous-time, continuous-state processes whose sample paths are everywhere continuous but nowhere differentiable. They arise in many natural phenomena and in some sense are generalized versions of the Brownian motion. The study of diffusion processes originated from the field of statistical physics, but diffusion processes have been used to model many physical, biological, engineering, economic, and social phenomena because diffusion is one of the fundamental mechanisms for transport of materials in physical, chemical, and biological systems. Also, many functions can be calculated explicitly for one-dimensional diffusion process. In the fields where diffusion has been applied, ...

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