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Stochastic integral of complex-valued processes. Levy's characterization of a multidimensional Brownian motion.
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Stochastic differential of a product.
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The multidimensional Ito-Doeblin formula
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General definition and properties of stochastic integral.
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Multidimensional stochastic integrals and Ito processes. Quadratic variation and cross variation.
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Multidimensional stochastic integrals: definition, linearity, mean and covariance matrix, martingale property, cross-variation.
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Cross-variation: definition. Cross-variation of independent and correlated Brownian motions.
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