Paul Lévy (mathematician)

Paul Pierre Lévy (15 September 1886 – 15 December 1971)

Lévy made many fundamental contributions to probability theory and the nascent theory of stochastic processes. He introduced the notion of 'stable distribution' which share the property of stability under addition of independent variables and proved a general version of the Central Limit theorem, recorded in his 1937 book Théorie de l'addition des variables aléatoires, using the notion of characteristic function. He also introduced, independently from Aleksandr Khinchin, the notion of infinitely divisible law and derived their characterization through the Lévy–Khintchine representation.

His 1948 monograph on Brownian motion, Processus stochastiques et mouvement brownien, contains a wealth of new concepts and results, including the Lévy area, the Lévy arcsine law, the local time of a Brownian path, and many other results.

Lévy received a number of honours, including membership at the French Academy of Sciences and honorary membership at the London Mathematical Society.

His daughter Marie-Hélène Schwartz and son-in-law Laurent Schwartz were also notable mathematicians.^[4]

Works

• 1922 – Lecons d'analyse Fonctionnelle
• 1925 – Calcul des probabilités
• 1937 – Théorie de l'addition des variables aléatoires
• 1948 – Processus stochastiques et mouvement brownien
• 1954 – Le mouvement brownien

See also

• Cramér's decomposition theorem
• Lévy distribution
• Lévy metric
• Lévy's modulus of continuity
• Lévy–Prokhorov metric
• Lévy's continuity theorem
• Lévy's zero-one law
• Concentration of measure
• Lévy process
• Lévy–Khintchine representation
• Lévy–Itô decomposition
• Lévy flight
• local time
• Isoperimetric inequality on a sphere
• Lévy's characterisation of Brownian motion

References