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# Limit Theorems in Theory of Stochastic Processes. Stochastic Differential Equations.

Descipline | Limit Theorems in Theory of Stochastic Processes. Stochastic Differential Equations. |

Faculty | Faculty of Mechanics and Mathematics |

Faculty URL | http://www.mechmat.univ.kiev.ua/en |

Language | English |

Degree | Master |

Credits | 5 |

Semester | 3 |

Description | The training course includes elements of the theory of weak convergence of probability distributions on metric spaces, the theory of weak convergence in the space C of continuous functions and in the space D of functions without discontinuities of 2-nd kind, Donsker’s and Skorokhod’s invariance principles, statistical applications of limit theorems for stochastic processes. The discipline studies the properties of Wiener process, theory of Ito’s stochastic integrals, Ito’s formula, existence and uniqueness theorems for solution to stochastic differential equation, strong and weak solution of stochastic differential equation, solutions to stochastic differential equation as Markov processes, diffusion processes and their properties, generator of a diffusion, the characteristic operator, stochastic differential equations depending on parameter, backward Kolmogorov’s equations, martingale problem, time change formula for Ito integrals, the Girsanov formula. |

Teachers | Borysenko Oleksandr Department of Probability Theory, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Phone: +380442590392 e-mail: odb@univ.kiev.ua |