This book develops the theory of continuous and discrete stochastic processes within the context of cell biology.  A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process – Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods. This text is primarily aimed at graduate students and researchers working in mathematical biology and applied mathematicians interested in stochastic modeling.  Applied probabilists and theoretical physicists should also find it of interest. It assumes no prior background in statistical physics and introduces concepts in stochastic processes via motivating biological applications. The book is highly illustrated and contains a large number of examples and exercises that further develop the models and ideas in the body of the text. It is based on a course that the author has taught at the University of Utah for many years.The second edition includes discussion of new topics such as the integrate-and-fire model of a neuron; microtubule catastrophes in bounded domains and first passage time problems; polymer dynamics, the Rouse model and nuclear organiation; stochastic models of transcriptional bursting and queuing theory; Synthetic gene networks including the repressilator; stochastic phase reduction methods; synchronization of genetic oscillators ; epigenetics, bacterial persistence and phase variation; the effects of cell growth and division on gene expression; Bacterial quorum sensing; diffusion in randomly switching environments; stochastic gap junctions; morphogen gradients; effects of diffusion on enzymatic reactions; the fundamental limits of cell signaling and linear response theory; noise-induced transitions in gene networks and epigenetics; discrete Markov chains; and large deviation theory.  weiterlesen