8.3 Stratonovich stochastic integrals and differential equations 192 8.3.1 The Stratonovich integral . ... 198 8.3.4 Changing variables . ... 259 11. 12. 10.5.1 The maximum . . . . . xiv Random processes: First-passage and escape.

Author: Jaume Masoliver

Publisher: World Scientific

ISBN: 9789813225336

Category: Mathematics

Page: 388

View: 256

Random processes are one of the most powerful tools in the study and understanding of countless phenomena in natural and social sciences.The book is a complete medium-level introduction to the subject. The book is written in a clear and pedagogical manner but with enough rigor and scope that can appeal to both students and researchers.This book is addressed to advanced students and professional researchers in many branches of science where level crossings and extremes appear but with some particular emphasis on some applications in socio-economic systems.

Stochastic RD processes • RD master equation • stochastic Turing patterns • path integral of RD master equation ... Wiener process and Ito stochastic calculus • Langevin and Fokker-Planck equations • first passage times • Kramers escape ...

Author: Paul C. Bressloff

Publisher: Springer Nature

ISBN: 9783030725198

Category: Biomathematics

Page: 724

View: 142

This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. In the second edition the material has been significantly expanded, particularly within the context of nonequilibrium and self-organizing systems. Given the amount of additional material, the book has been divided into two volumes, with volume I mainly covering molecular processes and volume II focusing on cellular processes. A wide range of biological topics are covered in the new edition, including stochastic ion channels and excitable systems, molecular motors, stochastic gene networks, genetic switches and oscillators, epigenetics, normal and anomalous diffusion in complex cellular environments, stochastically-gated diffusion, active intracellular transport, signal transduction, cell sensing, bacterial chemotaxis, intracellular pattern formation, cell polarization, cell mechanics, biological polymers and membranes, nuclear structure and dynamics, biological condensates, molecular aggregation and nucleation, cellular length control, cell mitosis, cell motility, cell adhesion, cytoneme-based morphogenesis, bacterial growth, and quorum sensing. The book also provides a pedagogical introduction to the theory of stochastic and nonequilibrium processes Fokker Planck equations, stochastic differential equations, stochastic calculus, master equations and jump Markov processes, birth-death processes, Poisson processes, first passage time problems, stochastic hybrid systems, queuing and renewal theory, narrow capture and escape, extreme statistics, search processes and stochastic resetting, exclusion processes, WKB methods, large deviation theory, path integrals, martingales and branching processes, numerical methods, linear response theory, phase separation, fluctuation-dissipation theorems, age-structured models, and statistical field theory. This text is primarily aimed at graduate students and researchers working in mathematical biology, statistical and biological physicists, and applied mathematicians interested in stochastic modeling. Applied probabilists should also find it of interest. It provides significant background material in applied mathematics and statistical physics, and introduces concepts in stochastic and nonequilibrium 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.

Escape. and. First. Passage. Problems. The possibility to calculate the probability density function or its moments ... One of the most important classes of other problem settings are the first passage problems for a stochastic process.

Author: Werner Ebeling

Publisher: World Scientific

ISBN: 9789810213824

Category: Science

Page: 329

View: 382

This book presents both the fundamentals and the major research topics in statistical physics of systems out of equilibrium. It summarizes different approaches to describe such systems on the thermodynamic and stochastic levels, and discusses a variety of areas including reactions, anomalous kinetics, and the behavior of self-propelling particles.

4.4 Stochastic and partial differential equations Many useful functionals of solutions of stochastic differential ... conditional and weighted expectations, functionals of the first passage times, escape probabilities from a given ...

Author: Zeev Schuss

Publisher: Springer Science & Business Media

ISBN: 9781441916051

Category: Mathematics

Page: 468

View: 789

Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular biophysics, communications theory and many more. Many books, reviews and research articles have been published on this topic, from the purely mathematical to the most practical. This book offers an analytical approach to stochastic processes that are most common in the physical and life sciences, as well as in optimal control and in the theory of filltering of signals from noisy measurements. Its aim is to make probability theory in function space readily accessible to scientists trained in the traditional methods of applied mathematics, such as integral, ordinary, and partial differential equations and asymptotic methods, rather than in probability and measure theory.

3.7 First Passage and Return Probabilities ... You can think of it as ''failure to escape the state. ... Definition Thefirst passage timefrom state ito state j, denoted Nij, is the (random variable) number of time steps necessary to ...

Author: James J. Solberg

Publisher: John Wiley & Sons

ISBN: 9780470322550

Category: Technology & Engineering

Page: 320

View: 420

By reducing mathematical detail and focusing on real-world applications, this book provides engineers with an easy-to-understand overview of stochastic modeling. An entire chapter is included on how to set up the problem, and then another complete chapter presents examples of applications before doing any math. A previously unpublished computational method for solving equations related to Markov processes is added. The book shows how to add costs or revenues to the basic probability structures without much additional effort. In addition, numerous examples are included that show how the theory can be used. Engineers will also find explanations on how to formulate word problems into the models that the math worked on.

Renormalization of first-passage times for random walks on deterministic fractals. Phys. Rev. ... Stochastic Processes in Physics and Chemistry (revised edition) (North-Holland. ... Thermally activated escape over fluctuating barriers.

Author: Sidney Redner

Publisher: Cambridge University Press

ISBN: 9780521652483

Category: Business & Economics

Page: 312

View: 542

The basic theory presented in a way which emphasizes intuition, problem-solving and the connections with other fields.

A very intricate analysis of mean square distances between zeros for a class of stationary stochastic processes is presented by Kac [7], a detailed account of which is beyond the scope of this book. B.4. The First Passage Time ...

Author: Soong

Publisher: Academic Press

ISBN: 9780080956121

Category: Computers

Page: 326

View: 533

Random Differential Equations in Science and Engineering

This distinction has many important implications for situations as diverse as chemical kinetics and stochastic search processes, where the rate at which an elemental event occurs is controlled by the first passage of a reactant or a ...

Author: Ralf Metzler

Publisher: World Scientific

ISBN: 9789814590303

Category: Mathematics

Page: 608

View: 703

The book contains review articles on recent advances in first-passage phenomena and applications contributed by leading international experts. It is intended for graduate students and researchers who are interested in learning about this intriguing and important topic. Contents:Arrival Statistics and Exploration Properties of Mortal Walkers (S B Yuste, E Abad and K Lindenberg)First Passage of a Randomly Accelerated Particle (T W Burkhardt)First Passage Problems in Anomalous Diffusion (A Rosso and A Zoia)First-Passage Times of Intermittent Random Walks (O Bénichou and R Voituriez)First-Passage Phenomena on Finite Inhomogeneous Networks (E Agliari and D Cassi)Effective Spectral Dimension in Scale-Free Networks (S Hwang, D-S Lee and B Kahng)First-Passage Statistics for Random Walks in Bounded Domains (R Voituriez and O Bénichou)First Passage Behavior of Multi-Dimensional Fractional Brownian Motion and Application to Reaction Phenomena (J-H Jeon, A V Chechkin and R Metzler)Trajectory-to-Trajectory Fluctuations in First-Passage Phenomena in Bounded Domains (T G Mattos, C Mejía-Monasterio, R Metzler, G Oshanin and G Schehr)Exact Record and Order Statists of Random Walk via First-Passage Ideas (G Schehr and S N Majumdar)First Passage in a Conical Geometry and Ordering of Brownian Particles (E Ben-Naim and P L Krapivsky)First Passage Time Problems in Biophysical Jump Processes with Fast Kinetics (P C Bressloff and J M Newby)First Passage Problems in Biology (T Chou and M R D'Orsogna)The Effect of Detection Mechanisms on Spatial Search and Foraging (D Campos and V Méndez)Search in Random Media with Lévy Flights (E Gelenbe and O H Abdelrahman)Exit Strategies: Visual Search and the Quitting Time Problem (T S Horowitz)Statistical Physics of Evolutionary Trajectories on Fitness Landscapes (M Manhart and A V Morozov)Some Applications of First-Passage Ideas to Finance (R Chicheportiche and J-P Bouchaud)First-Passage and Extremes in Socio-Economic Systems (J Masoliver and J Perelló)Transport and the First-Passage Time Problem with Application to Cold Atoms in Optical Traps (E Barkai and D A Kessler)The Excursion Set Theory in Cosmology (M Maggiore and A Riottoo)Self-Organized Escape Processes of Linear Chains in Nonlinear Potentials (T Gross, D Hennig and L Schimansky-Geier)Efficient Monte Carlo Methods for Simulating Diffusion-Reaction Processes in Complex Systems (D S Grebenkov) Readership: Researchers in stochastic processes, statistical physics, and mathematical physics. Key Features:Comprehensive update of the classical book by Sidney RednerApplications to wide-ranging and active fields of researchWell-known authors in the fieldKeywords:First Passage;Stochastic Processes;Diffusion;Biophysics;Non-Equilibrium Statistical Mechanics;Complex Systems;Econophysics

Effect of boundaries and defects on stochastic processes 5.1. ... Higher dimensional first passage times, return probabilities and escape probabilities; Polya's problem 6.3 Mean number of distinct points visited by a lattice walker in n ...

Author: E Montroll

Publisher: Elsevier

ISBN: 9780444601568

Category: Mathematics

Page: 356

View: 874

Studies in Statistical Mechanics, Volume VII: Fluctuation Phenomena Fluctuation explores different aspects of fluctuation behavior and their relation to microscopic processes and other phenomena, including the nucleation of a new phase following the quenching of a system into the coexistence region. It looks at phenomenological fluctuation theories, stochastic processes such as Markoff and momentless processes, and stochastic geometric aspects of amorphous solids. Comprised of five chapters, this volume begins with an overview of fluctuations and the Ehrenfest dog-flea model. It then turns to a discussion of density fluctuations in dilute gases, the Langevin theory of Brownian motion, and classical diffusion and random walks. It also systematically introduces the reader to the statistical mechanical theory of the kinetics of phase transitions, the molecular theory of metastability, and multidimensional continuous time random walks, along with the effect of boundaries and defects onf stochastic processes. In addition, it describes the phenomenological theory of the kinetics of nucleation and its application to nucleation, spinodal decomposition, and condensation. Other chapters focus on a stochastic model for the kinetics of phase transitions, the physical ideas used in theories of metastability, and the importance of dynamics in the study of metastability. The book explains how to estimate the escape rate and describes the statistical mechanics of clusters before concluding with a discussion of slowly-varying ensembles. This book is a valuable resource for students, physicists, and researchers who want to gain more knowledge and learn about statistical mechanics in general and fluctuation phenomena in particular.

Author: Ramon Castañeda-PriegoPublish On: 2021-09-13

... random walker undergoes escaping processes, characterized by an escape , instead of the mean first passage time. ... is important to highlight the relation between the escape time problem and the parameters of such stochastic model.