Complete list of publications of Tijana Levajković

1. Peer-reviewed scientific publications

1.1 Book

• T. Levajković, H. Men, Equations involving Malliavin calculus operators: Applications and numerical approximation. SpringerBriefs in Mathematics. Springer, Cham, 132 pp., ISBN: 978-3-319-65677-9, 2017.

1.2. Publications in refereed Journals

• T. Levajković, M. Messer, Multiscale change point detection via gradual bandwidth adjustment in moving sum processes, Electronic Journal of Statistics, Vol. 17, No. 1, 70-101, 2023.
• S. Gordić, T. Levajković, Lj. Oparnica, On a Wick-type stochastic parabolic equation with random potentials, Partial Differential Equations in Applied Mathematics Vol. 7, 100473, 2023.
• S. Gordić, T. Levajković, Lj. Oparnica, Stochastic parabolic evolution equations with singular potentials, Chaos, Solitons & Fractals, 111245, 2021.
• A. Kofler, T. Levajković, H. Mena, A. Ostermann, A splitting/ polynomial chaos expansion approach for stochastic evolution equations. J. Evol. Equ. 21, 1345–1381, 2021.
• T. Levajković, S. Pilipović, D. Seleši, M. Žigić, Stochastic evolution equations with Wick-polynomial nonlinearities. Electron. J. Probab. 23(116), 1-25, 2018.
• T. Levajković, H. Mena, L.-M. Pfurtscheller, Solving infinite dimensional stochastic LQR problems by polynomial chaos, IEEE Control Systems Letters 2(4), 641-646, 2018.
• C. Hafizoglu, I. Lasiecka, T. Levajković, H. Mena, A. Tuffaha, The stochastic linear quadratic problem with singular estimates. SIAM J. Control Optim. 55(2), 595-626, 2017.
• T. Levajković, D. Seleši, Malliavin calculus for generalized and test processes. Filomat 31(13), 4231-4256, 2017.
• R. Altmann, T. Levajković, H. Mena, Operator differential algebraic equations with noise appearing in fluid dynamics. Monatsh. Math. 182(4), 741–780, 2017.
• T. Levajković, H. Mena, A. Tuffaha, A numerical approximation frame- work for the stochastic linear quadratic regulator problem on Hilbert spaces. Appl. Math. Optim. 75(3), 499-523, 2017.
• T. Levajković, H. Mena, M. Zarfl, L´evy processes, subordinators and crime modelling. Novi Sad J. Math. 46(2), 65-86, 2016.
• T. Levajković, H. Mena, A. Tuffaha, The stochastic linear quadratic control problem: a chaos expansion approach. Evol. Equ. Control Theory 5(1), 105-134, 2016.
• T. Levajković, S. Pilipović, D. Seleši, Fundamental equations with higher order Malliavin operators. Stochastic 88(1), 106–127, 2016.
• T. Levajković, S. Pilipović, D. Seleši, Chaos expansion methods in Malliavin calculus: A survey of recent results. Novi Sad J. Math. 45(1), 45-103, 2015.
• T. Levajković, S. Pilipović, D. Seleši, Corrigendum and addendum to ”Chaos expansion methods in Malliavin calculus: A survey of recent results”. Novi Sad J. Math. 46(1), 227, 2016.
• T. Levajković, S. Pilipović, D. Seleši, M. Žigić, Stochastic evolution equations with multiplicative noise. Electron. J. Probab. 20(19), 1-23, 2015.
• T. Levajković, D. Seleši, Chaos expansion methods of stochastic processes for Malliavin-type equations. Electronic Notes in Discrete Mathematics 43, Elsevier, 289-298, 2013.
• T. Levajković, D. Seleši, Chaos expansion methods for stochastic differential equations involving the Malliavin derivative Part II. Publ. Inst. Math. 90, 85-98, 2011.
• T. Levajković, D. Seleši, Chaos expansion methods for stochastic differential equations involving the Malliavin derivative Part I. Publ. Inst. Math. 90, 65-84, 2011.
• T. Levajković, S. Pilipović, D. Seleši, The stochastic Dirichlet problem driven by the Ornstein-Uhlenbeck operator: Approach by the Fredholm alternative for chaos expansions. Stoch. Anal. Appl. 29, 317-331, 2011.
• T. Levajković, S. Pilipović, D. Seleši, Chaos expansions: Applications to a generalized eigenvalue problem for the Malliavin derivative. Integral Transforms Spec. Funct. 22(2), 97-105, 2011.

• 1.3. Book chapters

• T. Levajković, H. Mena, A. Tuffaha, The stochastic LQR optimal control with fractional Brownian motion, in M. Oberguggenberger, J. Toft, J. Vindas, P. Wahlberg (Eds.) Advanced in Partial Differen- tial Equations, Generalized Functions and Fourier Analysis, Dedicated to Stevan Pilipovi´c on the Occasion of his 65th Birthday, 115-151, Birkh¨auser, 2017.
• T. Levajković, H. Mena, Equations involving Malliavin derivative: A chaos expansion approach, in S. Pilipovi´c, J. Toft (Eds.) Pseudo- Differential Operators and Generalized Functions, Operator Theory: Advances and Applications, Vol. 245, 197–214, Springer International Publishing, 2015.
• T. Levajković, H. Mena, On deterministic and stochastic linear quadratic control problems, in V. Mityushev, M. Ruzhansky (Eds.), Current Trends in Analysis and Its Applications, Trends in Mathematics, Re- search Perspectives, pp. 315-322, Springer International Publishing Switzerland, 2015.
• T. Levajković, D. Seleši, Nonhomogeneous first order linear Malliavin type differential equation, in S. Molahajloo, S. Pilipovi´c, J. Toft, M. W. Wong (Eds.), Pseudo-Differential Operators: Generalized Functions and Asymptotic, pp. 353-369, Springer, 2013.

2. Theses

2.1. Habilitation

• Polynomial chaos expansion approach for stochastic partial differential equations with applications. Cumulative Habilitation Thesis, University of Innsbruck, Austria, 2020.

2.2. Dissertation

• Malliavin calculus for chaos expansions of generalized stochastic processes with applications to some classes of differential equations. Ph.D. Dissertation, University of Novi Sad, Serbia, 2012.

3. Software

• T. Levajkovi´c, M. Messer, mscp: Multiscale Change Point Detection via Gradual Bandwidth Adjustment in Moving Sum Processes. R package version 1.0, 2021.