Search for tag: "stochastic integral"

Brownian motion. Nondifferentiability of paths. The stochastic integral and the Ito isometry.

Stochastic integral of complex-valued processes. Levy's characterization of a multidimensional Brownian motion.

General definition and properties of stochastic integral.

Multidimensional stochastic integrals and Ito processes. Quadratic variation and cross variation.

Definition of local martingale. Construction of the stochastic integral for a process with locally square integrable sample paths.

Stopped stochastic processes. A stopped continuous martingale is a martingale. Properties of stopped stochastic integrals.

Multidimensional stochastic integrals: definition, linearity, mean and covariance matrix, martingale property, cross-variation.

Stochastic integral with respect to an Ito process. The Ito-Doeblin formula. Quadratic variation of an Ito process.

Stochastic integrals of simple processes. Stochastic integral of Brownian motion.

The partition property. Covariance and conditional covariance of stochastic integrals.

The stochastic integral is a continuous martingale.

The space M^2([0,T]). General definition of stochastic integral as a L^2 limit. Quadratic variation of a stochastic integral.