By Sidney Redner

ISBN-10: 0521036917

ISBN-13: 9780521036917

"...original and refreshing..." magazine of Mathematical Pyschology"This is the 1st publication totally dedicated to first-passage processes... good designed and typeset, [it] is written in an easy-to-read variety with a beneficiant collection of essentially drawn graphs. The e-book is especially invaluable for a person operating within the sector of stochastic processes." Mathematical Reviews"...clearly written...the organization and presentation of the cloth are excellent...a helpful repository of ordinary and not-so-standard thoughts which an individual operating within the quarter of stochastic techniques in most cases, and first-passage difficulties specifically, should want to have on their shelves." --Alan Bray, magazine of Statistical Physics"Unquestionably a worthy ebook, written at an available point for graduate scholars whereas delivering a pleasant precis of the final century's--and particularly the final decades'--developments of those equipment. It fills a gap within the literature that is wanted filling for no less than ten years. furthermore, the author's kind is secure and crystal transparent whereas protecting mathematical precision and power." --Charles Doering, collage of Michigan"to practitioners within the box of first- passage difficulties, and to scholars getting into the field...I can suggest it strongly. it truly is truly written, and the enterprise and presentation of the fabric are first-class. It serves as an invaluable repository of ordinary and not-so-standard options which someone operating within the zone of stochastic technique commonly, and first-passage difficulties particularly, should want to have on their shelves." Alan J. Bray, Dept of Physics and Astronomy, collage of Manchester, UK"Redner's strategy is often remarkably transparent and it is usually aimed to increase intuition....The ebook is explicitly meant for permitting people with a modest heritage to profit crucial effects fast. This target intrinsically locations it at the border among the class of textbooks and that of reference books. The author's type, colloquial and concise, but designated, is definately acceptable for the purpose." Paolo Laureti, Econophysics"The e-book is particularly good written and gives transparent reasons of the innovations used to figure out first passage possibilities and similar amounts, less than quite a few circumstances...this e-book [is] hugely advised to somebody drawn to its topic, either for its readability of presentation and for the wide variety of difficulties treated." J.R. Dorfman, American magazine of Physics First-passage houses underlie quite a lot of stochastic methods, reminiscent of diffusion-limited development, neuron firing, and the triggering of inventory ideas. This publication presents a unified presentation of first-passage approaches, which highlights its interrelations with electrostatics and the ensuing robust outcomes. the writer starts with a contemporary presentation of basic concept together with the relationship among the career and first-passage possibilities of a random stroll, and the relationship to electrostatics and present flows in resistor networks. the implications of this conception are then built for easy, illustrative geometries together with the finite and semi-infinite durations, fractal networks, round geometries and the wedge. quite a few functions are awarded together with neuron dynamics, self-organized criticality, diffusion-limited aggregation, the dynamics of spin platforms, and the kinetics of diffusion-controlled reactions. Examples mentioned contain neuron dynamics, self-organized criticality, kinetics of spin structures, and stochastic resonance.

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**Additional resources for A guide to first-passage processes**

**Example text**

Let k be the capacity level selected, in units of production per time unit. The firm then incurs a labor cost of wk dollars per time unit ever afterward, where w > 0 is a specified wage rate, even if it occasionally chooses to operate below capacity. 8). In addition to its labor costs, the firm incurs a materials cost of m dollars per unit of actual production. Given the initial capacity decision (workforce level), labor costs are fixed, and thus the marginal cost of production is m dollars per unit.

This means that X is a standard Brownian motion if and only if Q satisfies certain conditions. Write out in precise mathematical form what those conditions are, and then show that X is a standard Brownian motion if and only if Q is the Wiener measure. Although this problem requires nothing more than shuffling definitions, it is difficult for those who have never dealt with stochastic processes in abstract terms. It requires that one understand the general distinction between a stochastic process and its distribution, and the specific distinction between standard Brownian motion and the Wiener measure.

2) by saying that X is a ( µ, σ) Brownian motion with starting state x under P x . Heuristically, one may think of P x (A) as the conditional probability of event A given that X0 = x. 3, which means that F is the P x -completion of C and F is the filtration generated by X. Also, let E x be the expectation operator associated with P x . That is, E x (Z ) := Ω Z(ω) P x (dω) for all measurable functions (random variables) Z : Ω → R such that the integral on the right exists. 2 The backward and forward equations 37 With this setup, the strong Markov property of X can be recast in the following form.

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