{"product_id":"a-course-of-stochastic-analysis-alexander-melnikov-9783032204813","title":"A Course of Stochastic Analysis","description":"This thoroughly updated second edition offers a unified, modern pathway from the Kolmogorov foundations of probability to the tools of stochastic calculus--and on to applications in finance, statistics, and risk. With clarity and breadth, it develops martingale and semimartingale theory alongside stochastic differential equations, keeping both discrete- and continuous-time viewpoints in play. What's new in the 2nd Edition \u003cul\u003e Optional Stochastic Analysis on non-\"usual\" filtrations: the first textbook presentation of optional processes on stochastic bases beyond the standard right-continuous, complete setting, with an accompanying optional stochastic calculus. Optional SDEs and stochastic exponentials\/logarithms: existence-uniqueness theory and product\/inverse rules, with financial modeling worked out in this optional-semimartingale framework. New applications: Stochastic Regression Analysis and Risk Theory, showing how optional tools yield estimation results and ruin-probability bounds in general settings. Expanded exercises with solutions: a substantially enlarged Supplement (Ch. 15) featuring problems that reinforce both core theory and applications. \u003c\/ul\u003e Designed for senior undergraduates, graduate students, and instructors, the book also serves researchers and practitioners who need a concise, example-driven route from measure-theoretic probability to the techniques used in finance, statistics, and risk modeling. Abundant worked examples and a comprehensive set of problems--with hints and solutions--make it ideal for self study or course adoption.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Alexander Melnikov\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 303220481X\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783032204813\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 06\/03\/2026\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 292\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.30lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.31h x 6.50w x 0.82d","brand":"Alexander Melnikov","offers":[{"title":"Hardcover","offer_id":49084100575487,"sku":"9783032204813","price":59.99,"currency_code":"USD","in_stock":true}],"url":"https:\/\/www.whiterainbookhouse.com\/products\/a-course-of-stochastic-analysis-alexander-melnikov-9783032204813","provider":"WR Book House","version":"1.0","type":"link"}