Sergey Lototsky

• 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

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

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

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

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.

Contracts and Grants Awarded

• Stochastic Partial Differential Equations: Theory and Applications, (NSF), Sergey Lototsky $180,000, 2007-2012
• CAREER: Stochastic Partial Differential Equations and Applications, (NSF), Sergey Lototsky $400,000, 2002-2008
• Sloan Research Fellowship, (Alfred P. Sloan Foundation), Sergey Lototsky $40,000, 2002-2007
• Numerical Methods and Statistical Inference for Complex Stochastic Systems, (ARO (Army)), Boris Rozovskii $15,000, 2002-2005
• Boundary Value Problems for Stochastic Parabolic Equations, (NSF), Sergey Lototsky $61,000, 1998-2002

Conference Presentations

• Second-order stochastic evolution equations with constant coefficients , IMA WorkshopTalk/Oral Presentation, Invited, Minneapolis, MN, 10/23/2012
• Parameter estimation in second-order continuous time linear autoregressions , ICERM WorkshopTalk/Oral Presentation, Invited, Providence, RI, 10/10/2012
• Malliavin Calculus and SPDEs in Higher Order Chaos Spaces , SIAM-UQ 2012, MS69Talk/Oral Presentation, Invited, Raleigh, NC, 04/05/2012
• Optimal Linear Filtering of Stochastic Partial Differential Equations , AMS Meeting No. 1071, special session on SPDEsTalk/Oral Presentation, Invited, University of Nevada, Las Vegas, 04/30/2011
• Mean-preserving stochastic renormalization of differential equations , Workshop on Stochastic Multiscale MethodsTalk/Oral Presentation, Invited, BIRS, Banff, Canada, 03/29/2011
• Parameter Estimation in Stochastic Equations That Are Second-Order In Time , SIAM Annual Meeting, MS 72Talk/Oral Presentation, Invited, Pittsburgh, 07/14/2010
• A Stochastic Burgers Equation: Brinning Together Chaos Expansion, Embedding Theorems, and Catalan Numbers , Workshop on Stochastic Partial Differential EquationsLecture/Seminar, Invited, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 01/2010
• Parameter Estimation In Stochastic Equations That Are Second-Order In Time , Southern California Probability SymposiumLecture/Seminar, Invited, UCI, 12/05/2009
• A Stochastic Burgers Equation: Brinning Together Chaos Expansion, Embedding Theorems, and Catalan Numbers , AMS Meeting No. 1051Talk/Oral Presentation, Invited, Baylor University, Waco, TX, 10/17/2009
• A Stochastic Burgers Equation: Brinning Together Chaos Expansion, Embedding Theorems, and Catalan Numbers , Workshop on Stochastic Multiscale MethodsLecture/Seminar, Invited, USC, 08/10/2009
• Identification of Linear Stochastic Systems that are Second Order in Time , International Conference on Random Dynamical SystemsLecture/Seminar, Invited, Chern Institute of Mathematics, Tianjin, China, 06/11/2009
• Parameter Estimation in Stochastic Hyperbolic Equations , SAPS VIITalk/Oral Presentation, Invited, University du Maine, 03/16/2009
• Non-traditional Stochastic Partial Differential Equations , SIAM Annual Meeting – MS97Talk/Oral Presentation, SIAM, Invited, San Diego. CA, 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 ApplicationsTalk/Oral Presentation, CIRM – International Center for Mathematics Resear, Invited, Levico Terme, Italy, 01/09/2008
• Parameter Estimation in Diagonalizable Bi-linear Stochastic Parabolic Equations , Workshop on Applications of SPDEsTalk/Oral Presentation, Royal Academy, Invited, Mittag-Lefler Institute, Sweden, 11/22/2007
• Stochastic Parabolic Equations of Full Second Order , SPDE WorkshopTalk/Oral Presentation, Royal Academy, Invited, Mittag-Lefler Institute, Sweden, 09/10/2007
• LDP for SPDEs: a martingale approach , Large Deviations ConferenceTalk/Oral Presentation, Invited, University of Michigan, 06/08/2007
• Estimating coefficients in stochastic parabolic equations , SPDE meetingTalk/Oral Presentation, Invited, Cornell University, 04/22/2007
• Parameter estimation in stochastic partial differential equations , Asymptotic statistics of stochastic processesTalk/Oral Presentation, Invited, University of Le Mans, France, 03/21/2007
• Stochastic integration with respect to Gaussian processes and fields , SPDE WorkshopTalk/Oral Presentation, Invited, Brown University, 10/21/2006

Other Presentations

• Parameter Estimation in Second-Order Continuous Time Linear Autoregressions, Probability Seminar, Raleigh, NC, 2011-2012
• Parameter Estimation in Second-Order Continuous Time Linear Autoregressions, Probability and Statistics Seminar, Los Angeles, 2011-2012
• Wick Product in the Stochastic Burgers Equation: A Curse or a Cure?, Probability Seminar, Providence, RI, 2010-2011
• Mean-preserving renormalization of differential equations, Probability and Statistics Seminar, Los Angeles, CA, 2010-2011
• Wick Product in The Stochastic Burgers Equation: A Curse or a Cure?, Probability Seminar, Baton Rouge, 2010-2011
• Parameter Estimation in Stochastic Equations That are Second-Order in Time, Probability Seminar , Providence, RI, 2009-2010
• A Random Change of Variables and Applications to the Stochastic Porous Medium Equation with Multiplicative Time Noise, Special Seminar, Wuhan, China, 2008-2009
• A Random Change of Variables and Applications to the Stochastic Porous Medium Equation with Multiplicative Time Noise, Applied Mathematics Colloquium, Chicago, IL, 2008-2009
• From Abstract Stochastic Integration to Concrete Stochastic Differential Equations , Stochastics Seminar, GA Tech, Atlanta, GA, 2007-2008
• A Cahnge of Variables in Stochastic Partial Differential Equations, Graduate Colloquim, USC, 2007-2008
• Stochastic Integration With Respect to Gaussian Processes and Fields, Probability and Stochastic Processes Seminar, Haifa, Israel, 2007-2008
• Stochastic Integration With Respect to Gaussian Processes and Fields, Financial Mathematics Seminar, Uppsala University, Sweden, 2007-2008
• Stochastic Integration With Respect to Gaussian Processes and Fields, Mittag-Lefler Seminar, Djursholm, Sweden, 2007-2008
• Stochastic parabolic equations of full second order, Joint Applied Mathematics/Probability seminar, Detroit, MI, 2006-2007
• Parameter Estimation for SPDEs, Seminar, Woburn, MA, 2006-2007
• Parameter Estimation for SPDEs, Probability Seminar, Paris, France, 2006-2007
• Stochastic integration with respect to Gaussian processes and fields, Stochastic Systems Seminar, Providence, RI, 2006-2007
• Stochastic integration with respect to Gaussian processes and fields, Probability Seminar, Detroit, MI, 2006-2007
• `Parameter estimation in stochastic partial differential equations, Optimization Seminar, Denver, CO, 2006-2007
• Parameter estimation in stochastic partial differential equations, Probability Seminar, Palo Alto, CA, 2006-2007

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 Chapters

• 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.

Office Hours

MWF : 11am-12pm

MWF : 9:9:30am and 11am-12pm

MWF : 9-10am

Monday, Wednesday, Friday : 10:30-11:30am

Monday, Friday : M 8-10am F 9:30-10:30am

Other Advisement or Time Devoted to Students

Co-advisor of the USC Math Club (Wednesdays, 1-3pm)

Co-advisor of the USC undergraduate math club;
training of the USC Putnam
team (Wednesdays, 1-3pm)

Advisor of the USC undergradute math club

Advisor of the USC undergraduate math club and the coach of the USC Putnam team

New mathematics graduate student orientation

Co-advisor of the USC undergraduate math club

New mathematics graduate student orientation

New mathematics graduate student orientation

Administrative Appointments

• Associate Vice-Chair for Statistics, 09/2013-12/2014
• Associate Vise-Chair for Applied Mathematics, 09/2005-08/2013

Committees

• OCAAA – The Provost Oversight Committee for Athletic Academic Affairs, 2013-2015
• Probability Theory Graduate Exam, 2011-2012
• Probability Theory Graduate Exam, 2010-2011
• Probability Theory Graduate Exam, 2008-2010
• Differential Equations Graduate Exam
  , 2004-2005

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 Partial Differential Equations: Analysis and Computations”, 2013 –
• 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 Publications

• Mathematical Reviews, Regular contributor, 01/2000 –