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Sergey Lototsky

Professor of Mathematics

Contact Information
E-mail: lototsky@math.usc.edu
Phone: (213) 740-2389
Office: KAP 248D

LINKS
Curriculum Vitae
Faculty Profile on Departmental Website
Personal Website
Course Information
 

Education

Ph.D. Applied Mathematics, University of Southern California, 1/1996
M.S. Physics, Moscow Institute of Physics and Technology, Moscow, Russia, 1/1992
 

Postdoctoral Training

C.L.E. Moore Instructor of Mathematics, Massachusetts Institute of Technology, 09/1997-07/2000  
Post-doctoral member , Institute for Mathematics and its Applications, University of Minnesota, 1996-1997   
 

Academic Appointment, Affiliation, and Employment History

Tenure Track Appointments

Professor of Mathematics, University of Southern California, 12/22/2006-  
Associate Professor of Mathematics, University of Southern California, 05/15/2003-12/22/2006  
Assistant Professor of Mathematics, University of Southern California, 01/01/2000-05/15/2003  
 

Visiting and Temporary Appointments

Visitng Scholar, Institut Mittag-Leffler, The Royal Swedish Academy of Sciences, 08/30/2007-12/15/2007  
Visiting Professor , Division of Applied Mathematics, Brown University, 02/01/2007-04/30/2007  
Visiting Scholar , Center for Mathematical Sciences, University of Wisconsin, 07/1999-08/1999  
 

PostDoctoral Appointments

C.L.E. Moore Instructor of Mathematics, Department of Mathematics, Massachusetts Institute of Technology, 09/1997-07/2000  
Post-doctoral member , Institute for Mathematics and its Applications, University of Minnesota, 1996-1997   
 

Description of Research

Summary Statement of Research Interests

Professor Lotosky studies probability theory, stochastic processes, nonlinear filtering, and stochastic partial differential equations. Most recently he has authored several papers regarding stochastic parabolic equations and nonlinear filtering using Galerkin Approximation and Wiener Chaos Decomposition.
 

Funded Research

Contracts and Grants Awarded

Stochastic Partial Differential Equations: Theory and Applications (NSF), Sergey Lototsky, $180,000, 07/01/2008-06/30/2012  
CAREER: Stochastic Partial Differential Equations and Applications (NSF), Sergey Lototsky, $400,000, 07/01/2003-06/30/2008  
Sloan Research Fellowship (Alfred P. Sloan Foundation), Sergey Lototsky, $40,000, 09/15/2002-09/15/2006  
Numerical Methods and Statistical Inference for Complex Stochastic Systems (ARO (Army)), Boris Rozovskii, Sergey Lototsky, $15,000, 06/01/2003-06/30/2005  
Boundary Value Problems for Stochastic Parabolic Equations (NSF), Sergey Lototsky, $61,000, 07/01/1999-02/28/2002  
 

Conferences and Other Presentations

Conference Presentations

"Second-order stochastic evolution equations with constant coefficients", IMA Workshop, Talk/Oral Presentation, Minneapolis, MN, Invited, 10/23/2012  
"Parameter estimation in second-order continuous time linear autoregressions", ICERM Workshop, Talk/Oral Presentation, Providence, RI, Invited, 10/10/2012  
"Malliavin Calculus and SPDEs in Higher Order Chaos Spaces", SIAM-UQ 2012, MS69, Talk/Oral Presentation, Raleigh, NC, Invited, 04/05/2012  
"Optimal Linear Filtering of Stochastic Partial Differential Equations", AMS Meeting No. 1071, special session on SPDEs, Talk/Oral Presentation, University of Nevada, Las Vegas, Invited, 04/30/2011  
"Mean-preserving stochastic renormalization of differential equations", Workshop on Stochastic Multiscale Methods, Talk/Oral Presentation, BIRS, Banff, Canada, Invited, 03/29/2011  
"Parameter Estimation in Stochastic Equations That Are Second-Order In Time", SIAM Annual Meeting, MS 72, Talk/Oral Presentation, Pittsburgh, Invited, 07/14/2010  
"A Stochastic Burgers Equation: Brinning Together Chaos Expansion, Embedding Theorems, and Catalan Numbers ", Workshop on Stochastic Partial Differential Equations, Lecture/Seminar, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, Invited, 01/2010  
"Parameter Estimation In Stochastic Equations That Are Second-Order In Time", Southern California Probability Symposium, Lecture/Seminar, UCI, Invited, 12/05/2009  
"A Stochastic Burgers Equation: Brinning Together Chaos Expansion, Embedding Theorems, and Catalan Numbers", AMS Meeting No. 1051, Talk/Oral Presentation, Baylor University, Waco, TX, Invited, 10/17/2009  
"A Stochastic Burgers Equation: Brinning Together Chaos Expansion, Embedding Theorems, and Catalan Numbers", Workshop on Stochastic Multiscale Methods, Lecture/Seminar, USC, Invited, 08/10/2009  
"Identification of Linear Stochastic Systems that are Second Order in Time", International Conference on Random Dynamical Systems, Lecture/Seminar, Chern Institute of Mathematics, Tianjin, China, Invited, 06/11/2009  
"Parameter Estimation in Stochastic Hyperbolic Equations", SAPS VII, Talk/Oral Presentation, University du Maine, Invited, 03/16/2009  
"Non-traditional Stochastic Partial Differential Equations ", SIAM Annual Meeting - MS97, Talk/Oral Presentation, San Diego. CA, SIAM, Invited, 07/11/2008  
"A Random Change of Variables and Applications to the Stochastic Porous Medium Equation with Multiplicative Time Noise", Stochastic Partial Differential Equations and Applications, Talk/Oral Presentation, Levico Terme, Italy, CIRM - International Center for Mathematics Resear, Invited, 01/09/2008  
"Parameter Estimation in Diagonalizable Bi-linear Stochastic Parabolic Equations", Workshop on Applications of SPDEs, Talk/Oral Presentation, Mittag-Lefler Institute, Sweden, Royal Academy, Invited, 11/22/2007  
"Stochastic Parabolic Equations of Full Second Order", SPDE Workshop, Talk/Oral Presentation, Mittag-Lefler Institute, Sweden, Royal Academy, Invited, 09/10/2007  
"LDP for SPDEs: a martingale approach", Large Deviations Conference, Talk/Oral Presentation, University of Michigan, Invited, 06/08/2007  
"Estimating coefficients in stochastic parabolic equations", SPDE meeting, Talk/Oral Presentation, Cornell University, Invited, 04/22/2007  
"Parameter estimation in stochastic partial differential equations", Asymptotic statistics of stochastic processes, Talk/Oral Presentation, University of Le Mans, France, Invited, 03/21/2007  
"Stochastic integration with respect to Gaussian processes and fields", SPDE Workshop, Talk/Oral Presentation, Brown University, Invited, 10/21/2006  
 

Other Presentations

"Parameter Estimation in Second-Order Continuous Time Linear Autoregressions", Probability Seminar, NC State University, Raleigh, NC, 04/04/2012  
"Parameter Estimation in Second-Order Continuous Time Linear Autoregressions", Probability and Statistics Seminar, USC, Los Angeles, 03/23/2012  
"Wick Product in the Stochastic Burgers Equation: A Curse or a Cure?", Probability Seminar, Division of Applied Mathematics, Brown University, Providence, RI, 04/19/2011  
"Mean-preserving renormalization of differential equations", Probability and Statistics Seminar, Department of Mathematics, USC, Los Angeles, CA, 03/25/2011  
"Wick Product in The Stochastic Burgers Equation: A Curse or a Cure?", Probability Seminar, Department of Mathematics, Louisiana State University, Baton Rouge, 12/03/2010  
"Parameter Estimation in Stochastic Equations That are Second-Order in Time", Probability Seminar , Division of Applied Mathematics, Brown University , Providence, RI, 04/20/2010  
"A Random Change of Variables and Applications to the Stochastic Porous Medium Equation with Multiplicative Time Noise", Special Seminar, Huazhong University of Science and Technology, Wuhan, China, 06/15/2009  
"A Random Change of Variables and Applications to the Stochastic Porous Medium Equation with Multiplicative Time Noise", Applied Mathematics Colloquium, Illinois Institute of Technology, Chicago, IL, 03/30/2009  
"From Abstract Stochastic Integration to Concrete Stochastic Differential Equations ", Stochastics Seminar, Department of Mathematics, GA Tech, Atlanta, GA, 03/28/2008  
"A Cahnge of Variables in Stochastic Partial Differential Equations", Graduate Colloquim, Department of Mathematics, USC, 03/10/2008  
"Stochastic Integration With Respect to Gaussian Processes and Fields", Probability and Stochastic Processes Seminar, Technion, Haifa, Israel, 12/25/2007  
"Stochastic Integration With Respect to Gaussian Processes and Fields", Financial Mathematics Seminar, Department of Mathematic, Uppsala University, Sweden, 11/26/2007  
"Stochastic Integration With Respect to Gaussian Processes and Fields", Mittag-Lefler Seminar, Mittag-Lefler Institute, Djursholm, Sweden, 09/18/2007  
"Stochastic parabolic equations of full second order", Joint Applied Mathematics/Probability seminar, Wayne State University, Detroit, MI, 06/07/2007  
"Parameter Estimation for SPDEs", Seminar, Scientific Systems Company, Inc. , Woburn, MA, 04/17/2007  
"Parameter Estimation for SPDEs", Probability Seminar, University Paris-VI, Paris, France, 03/20/2007  
"Stochastic integration with respect to Gaussian processes and fields", Stochastic Systems Seminar, Brown University, Providence, RI, 03/06/2007  
"Stochastic integration with respect to Gaussian processes and fields", Probability Seminar, Wayne State University, Detroit, MI, 02/28/2007  
"`Parameter estimation in stochastic partial differential equations", Optimization Seminar, Univesity of Colorado, Denver, CO, 01/23/2007  
"Parameter estimation in stochastic partial differential equations", Probability Seminar, Stanford University, Palo Alto, CA, 01/08/2007  
 

Publications

Book

P. H. Baxendale, S. V. Lototsky (Ed.). (2007). Stochastic Differential Equations: Theory and Applications. (Vol. 2, Singapore: World Scientific. PubMed Web Address
Blum, E. K., Lototsky, S. V. (2006). Mathematics of Physics and Engineering. World Scientific. http://www.amazon.co.uk/exec/obidos/ASIN/981256621X/026-3154333-2129236
 

Book Chapter

Lototsky, S. V. (2011). Chaos Approach to Nonlinear Filtering. The Oxford Handbook of Nonlinear Filtering pp. 231-264. Oxford University Press.
Lototsky, S. V., Rozovskii, B. L. (2007). Stochastic Parabolic Equations of Full Second Order. (Vol. 145). pp. 199-210. Minneapolis, MN: IMA.
Lototsky, S. V., Rozovskii, B. L. (2006). Stochastic Differential Equations: A Wiener Chaos Approach. pp. 433-507. Springer.
Lototsky, S. V. (2004). Optimal Filtering of Stochastic Parabolic Equations. pp. 330-353. World Scientific.
 

Journal Article

Lin, N., Lototsky, S. V. (2014). Second-order continuous-time non-stationary Gaussian autoregression. Statistical Inference for Stochastic Processes. Vol. 17 (1)
Lototsky, S. V., Zhong, J. (2013). Stochastic Evolution Systems With Constant Coefficients. Stochastic Partial Differential Equations: Analysis and Computations. Vol. 1 (4), pp. 687-711.
Lototsky, S. V., Rozovskii, B. L., Selesi, D. (2012). On generalized Malliavin calculus. Stochastic Processes and their Applications. Vol. 122 (3), pp. 808-843.
Kaligotla, S., Lototsky, S. V. (2011). Wick Product in The Stochastic Burgers Equation: A Curse or a Cure?. Asymptotic Analysis. Vol. 75 (3-4), pp. 145-168.
Lin, N., Lototsky, S. V. (2011). Undamped Harmonic Oscillator Driven by Additive Gaussian White Noise: A Statistical Analysis. Communications on Stochastic Analysis. Vol. 5 (1), pp. 233-250.
Liu, W., Lototsky, S. V. (2010). Parameter Estimation in Hyperbolic Multichannel Models. Asymptotic Analysis. Vol. 68 (4), pp. 223-248.
Lototsky, S. V., Rozovskii, B. L., Wan, X. (2010). Elliptic Equations of Higher Stochastic Order. ESAIM: Mathematical Modelling and Numerical Analysis. Vol. 44 (5), pp. 1135-1153.
Lototsky, S. V., Rozovskii, B. (2010). A Unified Approach to Stochastic Evolution Equations Using the Skorokhod Integral. Theory of Probability and its Applications. Vol. 54 (2), pp. 189-202.
Lototsky, S. V. (2009). Statistical Inference for Stochastic Parabolic Equations: A Spectral Approach. Publicacions Matematiques. Vol. 53 (1), pp. 3–45.
Stemmann, K., Lototsky, S. V. (2009). Stochastic Integrals and Evolution Equations with Gaussian Random Fields. Applied Mathematics and Optimization. Vol. 59 (2), pp. 203-232.
Cialenco, I., Lototsky, S. V., Pospisil, J. (2009). Asymptotic Properties of the Maximum Likelihood Estimator for Stochastic Parabolic Equations with Additive Fractional Brownian Motion. Stochastics and Dynamics. Vol. 9 (2), pp. 169-185.
Lototsky, S. V., Rozovskii, B. L. (2009). Stochastic Differential Equations Driven by Purely Spatial Noise. SIAM J Math. Anal. Vol. 41 (4), pp. 1295-1322.
Cialenco, I., Lototsky, S. V. (2009). Parameter Estimation in Diagonalizable Bilinear Stochastic Parabolic Equations. Statistical Inference for Stochastic Processes. Vol. 12 (3), pp. 203-219.
Lototsky, S. V., Stemmann, K. (2008). Solving SPDEs Driven by Colored Noise: a Chaos Approach. Quartely of Applied Mathematics. Vol. 66 (3), pp. 499-520.
Lototsky, S. V. (2007). A Random Change of Variables and Applications to the Stochastic Porous Medium Equation with Multiplicative Time Noise. Communications on Stochastic Analysis. Vol. 1 (3), pp. 343-355.
Lototsky, S. V., Rozovsky, B. L. (2006). Wiener Chaos Solutions of Linear Stochastic Evolution Equations. Annals of Probability. Vol. Vol. 34 (No. 2 - March 2006)
Lototsky, S. V. (2006). Wiener Chaos and Nonlinear Filtering. No Journal Defined. Vol. NA
Lototsky, S. V., Rozovskii, B. L. (2004). Passive Scalar Equation in a Turbulent Incompressible Gaussian Velocity Field. Russian Mathematical Surveys. Vol. 59 (2), pp. 297-312.
Lototsky, S. V. (2003). Nonlinear Filtering of Diffusion Processes in Correlated Noise: Analysis by Separation of Variables. Applied Mathematics and Optimization. Vol. 47 (2), pp. 167-194.
Lototsky, S. V. (2003). Parameter Estimation for Stochastic Parabolic Equations: Asymptotic Properties of a Two-Dimensional Projection Based Estimator. Statistical Inference for Stochastic Processes. Vol. 6 (1), pp. 65-87.
Lototsky, S. V. (2002). Small perturbation of stochastic parabolic equations: a power series analysis. Journal of Functional Analysis. Vol. 193 (1), pp. 94-115.
Lototsky, S. V. (2001). Linear Stochastic Parabolic Equations, Degenerating at the Boundary. Electronic Journal of Probability. Vol. 6 (24), pp. 14.
 

Other

Vadim Kaloshin, Sergey Lototsky, Michael, Roeckner (Ed.). (2006). Stochastic Dynamics in Finite and Infinite Dimensions. Discrete and Continuous Dynamical Systems - B.
 

Advisement

 

Other Advisement or Time Devoted to Students

Co-advisor of the USC Math Club (Wednesdays, 1-3pm), Spring 2011   
Co-advisor of the USC undergraduate math club; training of the USC Putnam team (Wednesdays, 1-3pm) , Fall 2010   
Advisor of the USC undergradute math club, Spring 2010   
Advisor of the USC undergraduate math club and the coach of the USC Putnam team, Fall 2009   
New mathematics graduate student orientation, 08/20/2009  
Co-advisor of the USC undergraduate math club , Fall 2008   
New mathematics graduate student orientation , 08/21/2008  
New mathematics graduate student orientation, 08/23/2007  
 

Service to the University

Administrative Appointments

Associate Vise-Chair for Applied Mathematics, 09/2005-  
 

Committees

Member, Probability Theory Graduate Exam, 2011-2012   
Chair, Probability Theory Graduate Exam, 2010-2011   
Member, Probability Theory Graduate Exam, 2008-2009  
Member, Differential Equations Graduate Exam , 2004-2005   
 

Service to the Profession

Conferences Organized

Principal Organizer, Inverse Problems in Stochastic Differential Equations, USC, 05/22/2007-05/26/2007  
Principal Organizer, Random Media and Stochastic Partial Differential Equations, USC, 06/14/2005-06/18/2005  
 

Editorships and Editorial Boards

Associate Editor, SIAM Journal on Mathematical Analysis, 07/2012-  
Associate Editor, Stochastics and Dynamics, 10/2008-  
Editorial Board - Member, IMS-Interdisciplinary Mathematical Sciences (World Scientific), 05/2008-  
 
 

Reviewer for Publication

Mathematical Reviews, AMS, Regular contributor, 01/2000-  
 
 
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