Search for tag: "brownian motion"

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Lecture 6.2: Levy-Processes and non-Gaussian… duration 1 hour 46 minutes Lecture 6.2: Levy-Processes and non-Gaussian… Lecture 6.2: Levy-Processes and non-Gaussian Ornstein-Uhlenbeck processes	Lecture 6.2: Levy-Processes and non-Gaussian Ornstein-Uhlenbeck processes Simulation of Poisson and compound Poisson processes. Simulation of subordinated Brownian motion and non-Gaussian Ornstein-Uhlenbeck processes. poisson process compound poisson process brownian motion ornstein-uhlenbeck process From Tiziano Vargiolu 3 plays 0
Lecture 2 - Simulation of basic processes duration 1 hour 36 minutes Lecture 2 - Simulation of basic processes Lecture 2 - Simulation of basic processes	Lecture 2 - Simulation of basic processes Examples: simulation from the multidimensional Gaussian law. Cholesky decomposition, PCA. Examples: generation of the skeleton of the multidimensional Brownian motion and the Ornstein-Uhlenbeck… gaussian vectors cholesky decomposition pca brownian motion ornstein-uhlenbeck process From Tiziano Vargiolu 8 plays 0
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 6: Functional limit theorems for… duration 1 hour 52 minutes Lecture 6: Functional limit theorems for… Lecture 6: Functional limit theorems for financial markets with long-range dependence	Lecture 6: Functional limit theorems for financial markets with long-range dependence * General conditions of weak convergence - Convergence of sums - Multiplicative scheme* Monotonicity along the diagonal of a triangular matrix in the Cholesky decomposition of a positive definite… weak convergence cholesky decomposition toeplitz matrix stationary processes fractional brownian motion high-frequency trading From Tiziano Vargiolu 8 plays 0
Lecture 2: Equations with unbounded coefficients… duration 1 hour 41 minutes Lecture 2: Equations with unbounded coefficients… Lecture 2: Equations with unbounded coefficients and H > 1/2	Lecture 2: Equations with unbounded coefficients and H > 1/2 1. Cox-Ingersoll-Ross equations with fBm. 2. Equations with unbounded drift. 3. Reflected Ornstein-Uhlenbeck equations. hurst coefficient drift cox-ingersoll-ross fractional brownian motion reflected processes ornstein-uhlenbeck From Tiziano Vargiolu 5 plays 0
Lecture 1: Standard stochastic differential… duration 1 hour 49 minutes Lecture 1: Standard stochastic differential… Lecture 1: Standard stochastic differential equations with fBm	Lecture 1: Standard stochastic differential equations with fBm 1. Integration with respect to fBm. 2. Elements of fractional and fractional stochastic calculus. 3. Stochastic differential equations with fBm and smooth coefficients. fractional brownian motion fractional calculus fractional stochastic calculus stochastic differential equations From Tiziano Vargiolu 32 plays 0
Lecture 62: martingale representation theorem duration 27 minutes 42 seconds Lecture 62: martingale representation theorem Lecture 62: martingale representation theorem	Lecture 62: martingale representation theorem The martingale representation theorem in the case of a multidimensional Brownian motion: representation of L^2 martingales and local martingales. martingale representation theorem local martingale filtration generated by a stochastic process brownian motion girsanov theorem girsanov kernel From Tiziano Vargiolu 24 plays 0
Lecture 58: the Girsanov theorem duration 33 minutes 33 seconds Lecture 58: the Girsanov theorem Lecture 58: the Girsanov theorem	Lecture 58: the Girsanov theorem The Girsanov theorem in the multidimensional case. Novikov's condition. girsanov theorem girsanov kernel equivalent probabilities brownian motion martingale property novikov condition From Tiziano Vargiolu 26 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 45: consequences of the Ito-Doeblin… duration 46 minutes 2 seconds Lecture 45: consequences of the Ito-Doeblin… Lecture 45: consequences of the Ito-Doeblin formula	Lecture 45: consequences of the Ito-Doeblin formula A note on the integrability in the Ito-Doeblin formula. The two-dimensional case. ito-doeblin formula correlated brownian motion From Tiziano Vargiolu 13 plays 0
Lecture 32: cross-variation duration 28 minutes 7 seconds Lecture 32: cross-variation Lecture 32: cross-variation	Lecture 32: cross-variation Cross-variation: definition. Cross-variation of independent and correlated Brownian motions. cross variation correlated brownian motion From Tiziano Vargiolu 17 plays 0
Lecture 31: the Cholesky decomposition duration 58 minutes 46 seconds Lecture 31: the Cholesky decomposition Lecture 31: the Cholesky decomposition	Lecture 31: the Cholesky decomposition The Cholesky decomposition correlated brownian motion correlation matrix cholesky decomposition From Tiziano Vargiolu 16 plays 0
Lecture 30: multidimensional Brownian motion duration 55 minutes 25 seconds Lecture 30: multidimensional Brownian motion Lecture 30: multidimensional Brownian motion	Lecture 30: multidimensional Brownian motion Definitions of multidimensional standard and correlated Brownian motions: correlation matrix. brownian motion correlated brownian motion correlation matrix From Tiziano Vargiolu 19 plays 0
Lectures 27-28: the Girsanov theorem and the… duration 1 hour 22 minutes Lectures 27-28: the Girsanov theorem and the… Lectures 27-28: the Girsanov theorem and the martingale representation theorem	Lectures 27-28: the Girsanov theorem and the martingale representation theorem Levy's characterization of Brownian motion. Drift transformation in the Brownian motion and the Girsanov theorem. The martingale representation theorem. Representation of densities of… levy's characterization theorem brownian motion girsanov theorem girsanov kernel drift martingale representation theorem equivalent probabilities density process density of probabilities From Tiziano Vargiolu 28 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