图书简介
This work was first drafted five years ago at the invitation of the editors of the Encyclopedia of Mathematics and its Applications. However, it was found to contain insufficient physical applications for that series; hence, it has finally come to rest at the doorstep of the American Mathematical Society. The first half of the work is little changed from the original, a fact which may partly explain both the allusions to applications and the elementary approach. It was written to be understood by a reader having minimal familiarity with continuous time stochastic processes. The most advanced prerequisite is an understanding of discrete parameter martingale convergence theorem. General summary and outline: 0. Introduction. Some gratuitous generalities on scientific method as it relates to diffusion theory. 1. Brownian motion is defined by the characterization of P. Lévy. Then it is constructed in three basic ways and these are proved to be equivalent in the appropriate sense. Uniqueness theorem. 2. Projective invariance and the Brownian bridge presented. Probabilistic and absolute properties are distinguished. Among the former: the distribution of the maximum, first passage time distributions, and fitting probabilities. Among the latter: law of created logarithm, quadratic variation, Hölder continuity, non-recurrence for (rgeq 2). 3. General methods of Markov processes adapted to diffusion. Analytic and probabilistic methods are distinguished. Among the former: transition functions, semigroups, generators, resolvents. Among the latter: Markov properties, stopping times, zero-or-one laws, Dynkin’s formula, additive functionals. 4. Classical modifications of Brownian motion. Absorption and the Dirichlet problem. Space-time process and the heat equation. Killed processes, Green functions, and the distributions of additive sectionals. Time-change theorem (classical case), parabolic equations and their solution semigroups, some basic examples, distribution of passage times. 5. Local time: construction by random walk embedding. Local time processes. Trotter’s theorem. The Brownian flow. Brownian excursions. The zero set and Lévy’s equivalence theorem. Local times of classical diffusions. Sample path properties. 6. Boundary conditions for Brownian motion. The general boundary conditions. Construction of the processes using local time. Green functions and eigenfunction expansions (compact case). 7. The chapter is a "finale" on nonsingular diffusion. The generators ((d/dm)(d^+/dx^+)) are characterized. The diffusions on open intervals are constructed. The conservative boundary conditions are obtained and their diffusions are constructed. The general additive functionals and nonconservative diffusions are developed and expressed in terms of Brownian motions. The audience for this survey includes anyone who desires an introduction to Markov processes with continuous paths that is both coherent and elementary. The approach is from the particular to the general. Each method is first explained in the simplest case and supported by examples. Therefore, the book should be readily understandable to anyone with a first course in measure-theoretic probability.
Trade Policy 买家须知
- 关于产品:
- ● 正版保障:本网站隶属于中国国际图书贸易集团公司,确保所有图书都是100%正版。
- ● 环保纸张:进口图书大多使用的都是环保轻型张,颜色偏黄,重量比较轻。
- ● 毛边版:即书翻页的地方,故意做成了参差不齐的样子,一般为精装版,更具收藏价值。
关于退换货:
- 由于预订产品的特殊性,采购订单正式发订后,买方不得无故取消全部或部分产品的订购。
- 由于进口图书的特殊性,发生以下情况的,请直接拒收货物,由快递返回:
- ● 外包装破损/发错货/少发货/图书外观破损/图书配件不全(例如:光盘等)
并请在工作日通过电话400-008-1110联系我们。
- 签收后,如发生以下情况,请在签收后的5个工作日内联系客服办理退换货:
- ● 缺页/错页/错印/脱线
关于发货时间:
- 一般情况下:
- ●【现货】 下单后48小时内由北京(库房)发出快递。
- ●【预订】【预售】下单后国外发货,到货时间预计5-8周左右,店铺默认中通快递,如需顺丰快递邮费到付。
- ● 需要开具发票的客户,发货时间可能在上述基础上再延后1-2个工作日(紧急发票需求,请联系010-68433105/3213);
- ● 如遇其他特殊原因,对发货时间有影响的,我们会第一时间在网站公告,敬请留意。
关于到货时间:
- 由于进口图书入境入库后,都是委托第三方快递发货,所以我们只能保证在规定时间内发出,但无法为您保证确切的到货时间。
- ● 主要城市一般2-4天
- ● 偏远地区一般4-7天
关于接听咨询电话的时间:
- 010-68433105/3213正常接听咨询电话的时间为:周一至周五上午8:30~下午5:00,周六、日及法定节假日休息,将无法接听来电,敬请谅解。
- 其它时间您也可以通过邮件联系我们:customer@readgo.cn,工作日会优先处理。
关于快递:
- ● 已付款订单:主要由中通、宅急送负责派送,订单进度查询请拨打010-68433105/3213。
本书暂无推荐
本书暂无推荐