Search for tag: "stochastic integral"

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Ph.D. course "The mathematics of energy… duration 1 hour 25 minutes Ph.D. course "The mathematics of energy… Ph.D. course "The mathematics of energy markets" - Lecture 4	Ph.D. course "The mathematics of energy markets" - Lecture 4 Brownian motion. Nondifferentiability of paths. The stochastic integral and the Ito isometry. brownian motion quadratic variation stochastic integral ito isometry From Tiziano Vargiolu 3 plays 0
Lecture 57: Levy's characterization duration 36 minutes 2 seconds Lecture 57: Levy's characterization Lecture 57: Levy's characterization	Lecture 57: Levy's characterization Stochastic integral of complex-valued processes. Levy's characterization of a multidimensional Brownian motion. complex-valued stochastic integral levy's characterization theorem cross variation quadratic variation martingale property brownian motion ito-doeblin formula From Tiziano Vargiolu 13 plays 0
Lecture 41: generalized stochastic integral duration 48 minutes 17 seconds Lecture 41: generalized stochastic integral Lecture 41: generalized stochastic integral	Lecture 41: generalized stochastic integral General definition and properties of stochastic integral. stochastic integral linearity local martingale quadratic variation cross variation From Tiziano Vargiolu 30 plays 0
Lecture 42: multidimensional Ito processes duration 34 minutes 40 seconds Lecture 42: multidimensional Ito processes Lecture 42: multidimensional Ito processes	Lecture 42: multidimensional Ito processes Multidimensional stochastic integrals and Ito processes. Quadratic variation and cross variation. stochastic integral ito process quadratic variation cross variation From Tiziano Vargiolu 20 plays 0
Lecture 40: local martingales duration 1 hour 8 minutes Lecture 40: local martingales Lecture 40: local martingales	Lecture 40: local martingales Definition of local martingale. Construction of the stochastic integral for a process with locally square integrable sample paths. local martingale stopping time stochastic integral From Tiziano Vargiolu 25 plays 0
Lecture 38: stopped stochastic processes duration 54 minutes 6 seconds Lecture 38: stopped stochastic processes Lecture 38: stopped stochastic processes	Lecture 38: stopped stochastic processes Stopped stochastic processes. A stopped continuous martingale is a martingale. Properties of stopped stochastic integrals. stopping time stopped process martingales supermartingale submartingale stochastic integral From Tiziano Vargiolu 25 plays 0
Lecture 34: multidimensional stochastic calculus duration 1 hour 22 minutes Lecture 34: multidimensional stochastic calculus Lecture 34: multidimensional stochastic calculus	Lecture 34: multidimensional stochastic calculus Multidimensional stochastic integrals: definition, linearity, mean and covariance matrix, martingale property, cross-variation. stochastic integral linearity covariance operator ito isometry martingale property cross variation From Tiziano Vargiolu 19 plays 0
Lecture 16: the Ito-Doeblin formula duration 1 hour 16 minutes Lecture 16: the Ito-Doeblin formula Lecture 16: the Ito-Doeblin formula	Lecture 16: the Ito-Doeblin formula Stochastic integral with respect to an Ito process. The Ito-Doeblin formula. Quadratic variation of an Ito process. stochastic integral quadratic variation ito-doeblin formula ito process brownian motion From Tiziano Vargiolu 30 plays 0
Lecture 12: examples of stochastic integrals duration 30 minutes 0 seconds Lecture 12: examples of stochastic integrals Lecture 12: examples of stochastic integrals	Lecture 12: examples of stochastic integrals Stochastic integrals of simple processes. Stochastic integral of Brownian motion. stochastic integral brownian motion simple processes quadratic variation From Tiziano Vargiolu 18 plays 0
Lecture 11: Stochastic integrals and conditioning duration 54 minutes 47 seconds Lecture 11: Stochastic integrals and conditioning Lecture 11: Stochastic integrals and conditioning	Lecture 11: Stochastic integrals and conditioning The partition property. Covariance and conditional covariance of stochastic integrals. partition property conditional expectation stochastic integral variance From Tiziano Vargiolu 21 plays 0
Lecture 9: stochastic integral as a stochastic… duration 33 minutes 39 seconds Lecture 9: stochastic integral as a stochastic… Lecture 9: stochastic integral as a stochastic process	Lecture 9: stochastic integral as a stochastic process The stochastic integral is a continuous martingale. continuity martingale property stochastic integral From Tiziano Vargiolu 22 plays 0
Lecture 10: stochastic integral for general… duration 48 minutes 54 seconds Lecture 10: stochastic integral for general… Lecture 10: stochastic integral for general processes	Lecture 10: stochastic integral for general processes The space M^2([0,T]). General definition of stochastic integral as a L^2 limit. Quadratic variation of a stochastic integral. stochastic integral cauchy sequence quadratic variation From Tiziano Vargiolu 23 plays 0