Mathematical translations

Mathematical texts in Chinese

A personal collection of mathematical lecture notes and books that I translate, revise, and typeset for Chinese-speaking mathematics students and researchers, arranged from foundational material to more advanced references.

Why I translate

Sharing good mathematics across languages

Alongside research and teaching, I translate and typeset French mathematical lecture notes that I particularly value. I do this as a personal interest, hoping to make carefully written French resources more accessible to mathematics students and researchers in China while preserving their notation, proofs, and mathematical voice.

Chinese edition

分析：积分理论、卷积、Fourier 与 Laplace 变换

Marc BRIANE · Gilles PAGÈS

An independent Chinese edition based on the eighth edition (2023) of Marc BRIANE and Gilles PAGÈS's L3–M1 textbook. Across 451 pages it develops measure theory and Lebesgue integration from foundational material through Lp spaces, Fubini and change-of-variables theorems, convolution, and Fourier and Laplace transforms, with exercises, multiple-choice questions, and exam problems.

Original authors: Marc BRIANE · Gilles PAGÈS
Chinese translation, revision, and typesetting: Yuguang XIAO（肖煜光）
Based on: Eighth French edition (2023) · De Boeck Supérieur
Contents: Measure theory · Lebesgue integration · Fourier and Laplace transforms

Open Chinese PDF Download PDF Original French book

This is an unofficial, non-commercial translation shared for study and exchange. Copyright in the original French book remains with its authors and publisher; the source is linked above.

Chinese edition

积分、概率与随机过程

Jean-François LE GALL

An independent Chinese edition based on Jean-François LE GALL's September 2006 lecture notes, carefully translated, checked, and typeset. Across 200 pages it develops integration and measure theory, probability, martingales, Markov chains, and an introduction to Brownian motion.

Original author: Jean-François LE GALL
Chinese translation, revision, and typesetting: Yuguang XIAO（肖煜光）
Based on: September 2006 French course notes
Contents: Integration · Probability · Stochastic processes

Open Chinese PDF Download PDF Original French notes

This is an unofficial, non-commercial translation shared for study and exchange. Copyright in the original French text remains with its author; the source is linked above.

Chinese edition

布朗运动、鞅与随机微积分

Jean-François LE GALL

An independent Chinese edition translated, revised, and typeset from Jean-François LE GALL's 2016 English edition. Across 257 pages it develops Gaussian processes, Brownian motion, martingales, continuous semimartingales, stochastic integration, Markov processes, connections with partial differential equations, stochastic differential equations, and local times, together with solutions to exercises.

Original author: Jean-François LE GALL
Chinese translation, revision, and typesetting: Yuguang XIAO（肖煜光）
Based on: 2016 English edition · Graduate Texts in Mathematics 274
Contents: Brownian motion · Martingales · Stochastic calculus

Open Chinese PDF Download PDF Original book

This is an unofficial, non-commercial translation shared for study and exchange. Copyright in the original English book remains with its author and publisher; the source is linked above.

Chinese edition

连续鞅与布朗运动

Daniel REVUZ · Marc YOR

An independent Chinese edition translated, revised, and typeset from the third edition, third corrected printing (2005) of Daniel REVUZ and Marc YOR's monograph. Across 632 pages it develops Brownian motion, martingales, Markov processes, stochastic integration, martingale representation, local times, time reversal, Girsanov theory, stochastic differential equations, additive functionals, Bessel processes, Ray–Knight theorems, excursion theory, and distributional limit theorems.

Original authors: Daniel REVUZ · Marc YOR
Chinese translation, revision, and typesetting: Yuguang XIAO（肖煜光）
Based on: Third edition, third corrected printing (2005) · Grundlehren 293
Contents: Brownian motion · Continuous martingales · Excursion theory

Open Chinese PDF Download PDF Original book

This is an unofficial, non-commercial translation shared for study and exchange. Copyright in the original English book remains with its authors and publisher; the source is linked above.