Kuznetsov, Sergei E.

Publications

selected publications

book
- Predelnye teoremy dlya sluchainykh protsessov. Tom 1. Ed. 47. 1994
- Predelnye teoremy dlya sluchainykh protsessov. Tom 2. Ed. 48. 1994
- Slozhnost bulevykh funktsii 1991
- Mnogomernyi statisticheskii analiz i veroyatnostnoe modelirovanie realnykh protsessov. Ed. 54. 1990
- Nizhnie otsenki slozhnosti i slozhnost universalnykh skhem 1990
chapter
- Boundary theory for superdiffusions. 323-330. 2002
- Solutions of a class of semilinear differential equations: trace and singularities on the boundary. 69-80. 1999
- Regularity properties of a supercritical superprocess. 221-235. 1994
- Representation d'un semi-groupe d'operateurs sur un espace L 1 par des noyaux. Remarques sur deux articles de S.E. kuznetsov. Lecture Notes in Mathematics. 304-311. 1993
- More on existence and uniquiness of decomposition of excessive functions and measures into extremes. Lecture Notes in Mathematics. 445-472. 1992
conference proceeding
- Homogeneous transition functions and dual semigroups. 327-330. 1987
journal article
- A class of boundary traces for solutions of the equation Lu = psi(u). Journal of Functional Analysis. 696-709. 2007
- Bessel capacities on compact manifolds and their relation to Poisson capacities. Journal of Functional Analysis. 281-294. 2007
- N-measures for branching exit Markov systems and their applications to differential equations. Probability Theory and Related Fields. 135-150. 2004
- An upper bound for positive solutions of the equation Delta u=u(alpha). Electronic Research Announcements in Mathematical Sciences. 103-112. 2004
- Poisson capacities. Mathematical Research Letters. 85-95. 2003

Teaching

courses taught

APPM 6550 - Introduction to Stochastic Processes
Primary Instructor - Spring 2024
Systematic study of Markov chains and some of the simpler Markov processes including renewal theory, limit theorems for Markov chains, branching processes, queuing theory, birth and death processes, and Brownian motion. Applications to physical and biological sciences. Department enforced prerequisite: MATH 4001 or MATH 4510 or APPM 3570 or APPM 4560 or instructor consent. Same as MATH 6550.
MATH 4510 - Introduction to Probability Theory
Primary Instructor - Fall 2019 / Fall 2021 / Spring 2022 / Fall 2022 / Fall 2023 / Fall 2024
Studies axioms, combinatorial analysis, independence and conditional probability, discrete and absolutely continuous distributions, expectation and distribution of functions of random variables, laws of large numbers, central limit theorems, and simple Markov chains if time permits. Degree credit not granted for this course and APPM 3570 or ECEN 3810 or MATH 3510. Same as MATH 5510.
MATH 4540 - Introduction to Time Series
Primary Instructor - Spring 2019 / Spring 2021 / Spring 2023
Studies basic properties, trend-based models, seasonal models, modeling and forecasting with ARIMA models, spectral analysis and frequency filtration. Same as MATH 5540 and STAT 4540 and STAT 5540.
MATH 5510 - Introduction to Probability Theory
Primary Instructor - Fall 2019 / Fall 2022 / Fall 2023 / Fall 2024
Studies axioms, combinatorial analysis, independence and conditional probability, discrete and absolutely continuous distributions, expectation and distribution of functions of random variables, laws of large numbers, central limit theorems, and simple Markov chains if time permits. Same as MATH 4510.
MATH 5540 - Introduction to Time Series
Primary Instructor - Spring 2021
Studies basic properties, trend-based models, seasonal models, modeling and forecasting with ARIMA models, spectral analysis and frequency filtration. Department enforced prerequisite: MATH 4520 or MATH 5520 or APPM 4520 or APPM 5520. Same as MATH 4540 and STAT 4540 and STAT 5540.

MATH 6310 - Introduction to Real Analysis 1
Primary Instructor - Fall 2019 / Fall 2020
Develops the theory of Lebesgue measure and the Lebesgue integral on the line, emphasizing the various notions of convergence and the standard convergence theorems. Applications are made to the classical L^p spaces. Department enforced prerequisite: MATH 4001. Instructor consent required for undergraduates.

MATH 6350 - Functions of a Complex Variable 1
Secondary Instructor - Spring 2024
Focuses on complex numbers and the complex plane. Includes Cauchy-Riemann equations, complex integration, Cauchy integral theory, infinite series and products, and residue theory. Department enforced prerequisite: MATH 4001. Instructor consent required for undergraduates.

MATH 6550 - Introduction to Stochastic Processes
Primary Instructor - Spring 2024
Systematic study of Markov chains and some of the simpler Markov processes, including renewal theory, limit theorems for Markov chains, branching processes, queuing theory, birth and death processes, and Brownian motion. Applications to physical and biological sciences. Department enforced prerequisite: MATH 4001 or MATH 4510 or APPM 3570 or APPM 4560. Instructor consent required for undergraduates. Same as APPM 6550.

STAT 4540 - Introduction to Time Series
Primary Instructor - Spring 2019 / Spring 2021 / Spring 2023
Studies basic properties, trend-based models, seasonal models modeling and forecasting with ARIMA models, spectral analysis and frequency filtration. Same as STAT 5540 and MATH 4540 and MATH 5540.

STAT 5540 - Introduction to Time Series
Primary Instructor - Spring 2019 / Spring 2021 / Spring 2023
Studies basic properties, trend-based models, seasonal models modeling and forecasting with ARIMA models, spectral analysis and frequency filtration. Department enforced prerequisite: APPM 5520 or MATH 5520. Recommended prerequisite: previous coursework equivalent to STAT 4520 or MATH 4520 or STAT 5520 or MATH 5520; minimum grade of C- for all. Same as STAT 4540 and MATH 4540 and MATH 5540.

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Background

education and training

D.Sc., Vilnius State Univ (Lithuania) 1983
Ph.D., Ukrainian Acad of Sciences, Inst of Math (Ukraine) 1976
M.S., Moscow State Univ (Russia) 1971

Other Profiles

ORCID iD

http://orcid.org/0000-0002-5247-0237

VIVO

Positions

Research Areas

Publications

selected publications

book

chapter

conference proceeding

journal article