Sergey Lototsky Professor of Mathematics Contact Information E-mail: lototsky@math.usc.edu Phone: (213) 740-2389 Office: DRB 258 Office Hours: Monday, Wednesday, Friday : 10:30-11:30am LINKS Curriculum Vitae Faculty Profile on Departmental Website Personal Website Course Information

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

Funded Research

Contracts and Grants Awarded

• Stochastic Partial Differential Equations: Theory and Applications (NSF), Sergey Lototsky, $180,000, 07/01/2008-06/30/2011  
• 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

• "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, Talk/Oral Presentation, , USC, Invited, 08/10/2009  
• "Identification of Linear Stochastic Systems that are Second Order in Time", International Conference on Random Dynamical Systems, Talk/Oral Presentation, , 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

• "A Stochastic Burgers Equation: Brinning Together Chaos Expansion, Embedding Theorems, and Catalan Numbers ", Special Seminar, Huazhong University of Science and Technology, Wuhan, China, 06/15/2009  
• "A Stochastic Burgers Equation: Brinning Together Chaos Expansion, Embedding Theorems, and Catalan Numbers ", 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., 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

• 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.
• 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

Office Hours

Other Advisement or Time Devoted to Students

• 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-  

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, Stochastics and Dynamics, 10/2008-  
• Editorial Board - Member, IMS-Interdisciplinary Mathematical Sciences (World Scientific), 05/2008-  

Reviewer for Publication

• Mathematical Reviews, AMS, 69 reviews so far; 3 during academic year 2008-2009, 01/2000-