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Applied Stochastic Analysis - NMTP533

Title:	Aplikovaná stochastická analýza
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2015 to 2017
Semester:	winter
E-Credits:	5
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	prof. RNDr. Bohdan Maslowski, DrSc.
Class:	M Mgr. PMSE M Mgr. PMSE > Povinně volitelné
Classification:	Mathematics > Probability and Statistics
Incompatibility :	NSTP240
Pre-requisite :	NMTP432
Interchangeability :	NSTP240
Is interchangeable with:	NSTP240

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: RNDr. Jitka Zichová, Dr. (24.04.2019)

In the present course stochastic linear and bilinear systems with countinuous time and continuous state space are studied. The course has been focused on three topics: a) optimal control for finite and infinite time horizon control problems b) fundamentals of filtering theory c) problems of inference, parameter estimation.

Aim of the course -

Last update: T_KPMS (16.05.2013)

The goal of the course is to present some basic achievements of the stochastic control and filtering theory and related topics for linear and bilinear multidimensional systems with continuous time and continuous state space

Literature - Czech

Last update: RNDr. Jitka Zichová, Dr. (24.04.2019)

[1] B. Oksendal: Stochastic Differential Equations, Springer-Verlag, 1985 (1. vyd.)

[2] W .H. Fleming and R. W .Rishel: Deterministic and Stochastic Optimal Control, Springer-Verlag, 1975

[3] J. Yong and X. Y. Zhou: Stochastic Controls, Hamiltonian Systems and HJB Equations, Springer-Verlag, 1999

[4] P. Mandl: Pravděpodobnostní dynamické modely, Academia, Praha, 1985

Teaching methods -

Last update: prof. RNDr. Bohdan Maslowski, DrSc. (25.09.2020)

Lecture+exercises.

Syllabus -

Last update: T_KPMS (16.05.2013)

1. LQ problem for linear and bilinear stochastic equations in a vector space

2. The linear filtering problem, Kalman - Bucy filter

3. Some methods of parameter estimation for linear stochastic systems, properties of estimators