First-passage process by Sidney Redner

By Sidney Redner

Preface; Errata; 1. First-passage basics; 2. First passage in an period; three. Semi-infinite approach; four. Illustrations of first passage in basic geometries; five. Fractal and nonfractal networks; 6. platforms with round symmetry; 7. Wedge domain names; eight. purposes to uncomplicated reactions; References; Index

Show description

Read or Download First-passage process PDF

Best stochastic modeling books

Handbook of statistics 19: Stochastic processes, theory and methods

Hardbound. J. Neyman, one of many pioneers in laying the rules of contemporary statistical concept, under pressure the significance of stochastic methods in a paper written in 1960 within the following phrases: "Currently within the interval of dynamic indeterminism in technological know-how, there's hardly ever a significant piece of analysis, if handled realistically, doesn't contain operations on stochastic processes".

Stochastic Dynamics of Reacting Biomolecules

This can be a publication in regards to the actual tactics in reacting complicated molecules, rather biomolecules. some time past decade scientists from diversified fields similar to medication, biology, chemistry and physics have amassed a big volume of information in regards to the constitution, dynamics and functioning of biomolecules.

Analytical and stochastic modeling techniques and applications 16th international conference, ASMTA 2009, Madrid, Spain, June 9-12, 2009: proceedings

This booklet constitutes the refereed complaints of the sixteenth overseas convention on Analytical and Stochastic Modeling concepts and functions, ASMTA 2009, held in Madrid, Spain, in June 2009 together with ECMS 2009, the 23nd eu convention on Modeling and Simulation. The 27 revised complete papers awarded have been rigorously reviewed and chosen from fifty five submissions.

Introduction to Stochastic Calculus Applied to Finance (Stochastic Modeling)

Lately the transforming into significance of by-product items monetary markets has elevated monetary associations' calls for for mathematical abilities. This booklet introduces the mathematical equipment of economic modeling with transparent causes of the main helpful types. advent to Stochastic Calculus starts with an trouble-free presentation of discrete versions, together with the Cox-Ross-Rubenstein version.

Extra resources for First-passage process

Sample text

The basic connection is that if all the lattice bonds are viewed as resistors (not necessarily identical), then Kirchhoff’s laws for steady current flow in the + + + + + + - - V + - + - + - + (a) (b) Fig. 5. (a) A lattice graph with boundary sites B+ or B− . (b) Corresponding resistor network in which each bond (with rectangle) is a 1- resistor. The sites in B+ are all fixed at potential V = 1, and sites in B− are all grounded. 34 First-Passage Fundamentals network are identical to the discrete Laplace equation for E.

The Green’s Function Formalism Let us recall the conventional method to compute the first-passage probability of diffusion. Consider a diffusing particle that starts at r 0 within a domain with boundary B. 1) with the initial condition c(r , 0; r 0 ) = δ(r − r 0 ) and the absorbing boundary condition c(r , t; r 0 )|r ∈B = 0. This condition accounts for the fact that once a particle reaches the boundary it leaves the system. Because the initial condition is invariably a single particle at r 0 , we will typically not write this argument in the Green’s function.

Because the voltage V j also equals the probability for the corresponding random walk to reach B+ without reaching B− , the term V j P+ j is just the probability that a random walk starts at B+ , makes a single step to the sites j (with hopping probabilities Pi j ), and then returns to B+ without reaching B− . We therefore deduce that I = (1 − V j )P+ j g+ j j = j g+ j × (1 − return probability) j g+ j × escape probability. 4) j Here “escape” means reaching the opposite terminal of the voltage source without returning to the starting point.

Download PDF sample

Rated 4.50 of 5 – based on 46 votes