II: 07, 123-139, LNM 51 (1968)
SAM LAZARO, José de
Sur les moments spectraux d'ordre supérieur (
Second order processes)
The essential result of the paper (Shiryaev,
Th. Prob. Appl.,
5, 1960; Sinai,
Th. Prob. Appl.,
8, 1963) is the definition of multiple stochastic integrals with respect to a second order process whose covariance satisfies suitable spectral properties
Keywords: Spectral representation,
Multiple stochastic integralsNature: Exposition
Retrieve article from Numdam
X: 17, 245-400, LNM 511 (1976)
MEYER, Paul-André
Un cours sur les intégrales stochastiques (6 chapters) (
Stochastic calculus,
Martingale theory,
General theory of processes)
This is a systematic exposition of the theory of stochastic integration with respect to semimartingales, with the exception of stochastic differential equations. Chapter I is devoted to a quick exposition of the general theory of processes, and of the trivial stochastic integral with respect to a process of finite variation. Chapter II is the Kunita-Watanabe theory of square integrables martingales, angle and square bracket, stable subspaces, compensated sums of jumps, and the corresponding $L^2$ theory of stochastic integration. Chapter III studies a restricted class of semimartingales and introduces the Ito formula, with its celebrated applications due to Watanabe, to Brownian motion and the Poisson process. Chapter IV localizes the theory and gives the general definitions of semimartingales and special semimartingales, and studies the stochastic exponential, multiplicative decomposition. It also sketches a theory of multiple stochastic integrals. Chapter V deals with the application of the spaces $H^1$ and $BMO$ to the theory of stochastic integration, and to martingales inequalities (it contains the extension to continuous time of Garsia's ``Fefferman implies Davis implies Burkholder'' approach). Chapter VI contains more special topics: Stratonovich integrals, Girsanov's theorem, local times, representation of elements of $BMO$
Comment: This set of lectures was well circulated in its time, an intermediate stage between a research paper and a polished book form. See also
1131. Now the material can be found in many books
Keywords: Increasing processes,
Stable subpaces,
Angle bracket,
Square bracket,
Stochastic integrals,
Optional stochastic integrals,
Previsible representation,
Change of variable formula,
Semimartingales,
Stochastic exponentials,
Multiplicative decomposition,
Fefferman inequality,
Davis inequality,
Stratonovich integrals,
Burkholder inequalities,
$BMO$,
Multiple stochastic integrals,
Girsanov's theoremNature: Exposition,
Original additions Retrieve article from Numdam
XLIII: 12, 309-325, LNM 2006 (2011)
TUDOR, Ciprian A.
Asymptotic Cramér's theorem and analysis on Wiener space (
Limit theorems,
Stochastic analysis)
Keywords: Multiple stochastic integrals,
Limit theorems,
Malliavin calculus,
Stein's methodNature: Original
XLV: 13, 323-351, LNM 2078 (2013)
BOURGUIN, Solesne;
TUDOR, Ciprian A.
Malliavin Calculus and Self Normalized Sums (
Theory of processes)
Keywords: Malliavin calculus,
Stein's method,
self-normalized sums,
limit theorems,
multiple stochastic integrals,
chaos expansionsNature: Original
