{"id":259,"date":"2023-06-11T21:27:14","date_gmt":"2023-06-12T04:27:14","guid":{"rendered":"https:\/\/live-usc-dornsife.pantheonsite.io\/sergey-lototsky\/?page_id=259"},"modified":"2023-11-16T11:26:55","modified_gmt":"2023-11-16T19:26:55","slug":"research","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/sergey-lototsky\/research\/","title":{"rendered":"Publications"},"content":{"rendered":"\n\n \n \n\n\n\n\n\n\n\n
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Books<\/h5>\n
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  1. B. L. Rozovsky and S. V. Lototsky. Stochastic Evolution Systems, Second Edition.<\/a> Springer, 2018.<\/li>\n
  2. S. V. Lototsky and B. L. Rozovsky. Stochastic Partial Differential Equations. Springer, 2017. At Springer<\/a> At Amazon.com<\/a><\/li>\n
  3. P. Baxendale and S. Lototsky, Editors. Stochastic Differential Equations: Theory and Applications. A volume in honor of Professor B. L. Rozovskii. <\/a>Volume 2 of the series “Interdisciplinary Mathematical Sciences”. World Scientific, 2007.<\/li>\n
  4. E. K. Blum and S. V. Lototsky. Mathematics of Physics and Engineering. World Scientific, 2006. At Amazon.com<\/a> At Barnes and Noble<\/a><\/li>\n<\/ol>\n
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    Papers<\/h5>\n
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    1. R. Sh. Liptser and S. V. Lototsky. Diffusion Approximation and Robust Kalman Filter, Journal of Mathematical Systems, Estimation and Control, Vol. 2, No. 3, pp. 263-274, 1992.<\/li>\n
    2. O. V. Gulinskii, R. Sh. Liptser, and S. V. Lototsky. Large Deviations for Unbounded Additive Functionals of Markov Processes with Discrete Time (non-compact case), Journal of Applied Mathematics and Stochastic Analysis, Vol. 7, No. 3, pp. 423-436, 1994.<\/li>\n
    3. S. V. Lototsky. Robust Algorithms of the Type of Stochastic Approximation (continuous time), Teoriya Veroyatnostei i ee Primeneninya. (Russian), Vol. 40, No. 2, pp. 324-346, 1995. English translation: Theory of Probability and its Applications (SIAM translation of the Russian journal), Vol. 40, No. 2, pp. 309-328, 1996.<\/li>\n
    4. S. V. Lototsky, C. Rao, and B. L. Rozovskii. Fast Nonlinear Filter for Continuous-Discrete Time Multiple Models, <\/a>Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan, Dec. 11-13, 1996, Vol. 4, pp. 4071-4076, Omnipress, Madison, WI.<\/li>\n
    5. S. V. Lototsky, R. Mikulevicius, and B. L. Rozovskii. Nonlinear Filtering Revisited: a Spectral Approach, II,<\/a> Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan, Dec. 11-13, 1996, Vol. 4, pp. 4060-4064, Omnipress, Madison, WI.<\/li>\n
    6. S. V. Lototsky, R. Mikulevicius, and B. L. Rozovskii. Nonlinear Filtering Revisited: a Spectral Approach <\/a>, SIAM Journal on Control and Optimization, Vol. 35, No. 2, pp. 435-461, March 1997.<\/li>\n
    7. S. V. Lototsky and B. L. Rozovskii. Recursive Multiple Wiener Integral Expansion for Nonlinear Filtering of Diffusion Processes <\/a>. In: J. A. Goldstein, N. E. Gretsky, and J. J. Uhl (editors), Stochastic Processes and Functional Analysis, pp. 199-208. Lecture notes in pure and applied mathematics, Vol. 186, Marcel Dekker, Inc., 1997.<\/li>\n
    8. M. Huebner, S. V. Lototsky, and B. L. Rozovskii. Asymptotic Properties of an Approximate Maximum Likelihood Estimator for Stochastic PDEs. <\/a>In: Yu. M. Kabanov, B. L. Rozovskii, and A. N. Shiryaev (editors), Statistics and Control of Stochastic Processes (the Liptser festschrift), pp. 139-155. World Scientific, 1997.<\/li>\n
    9. S. V. Lototsky and B. L. Rozovskii. Recursive Nonlinear Filter for a Continuous – Discrete Time Model: Separation of Parameters and Observations, <\/a>IEEE Transactions on Automatic Control, Vol. 43, No. 8, pp. 1154-1158, August 1998.<\/li>\n
    10. N. V. Krylov and S. V. Lototsky. A Sobolev Space Theory of SPDEs with Constant Coefficients on a Half Line. <\/a>SIAM Journal on Mathematical Analysis. Vol. 30, No. 2, pp. 298-325, March 1999.<\/li>\n
    11. S. V. Lototsky and B. L. Rozovskii. Spectral Asymptotics of Some Functionals Arising in Statistical Inference for SPDEs. <\/a>Stochastic Processes and Their Application, Vol. 79, No. 1, pp. 69-94, 1999.<\/li>\n
    12. N. V. Krylov and S. V. Lototsky. A Sobolev Space Theory of SPDEs with Constant Coefficients in a Half Space. <\/a>SIAM Journal on Mathematical Analysis, Vol. 31, No. 1, pp. 19-33, 2000.<\/li>\n
    13. S. V. Lototsky. Dirichlet Problem for Stochastic Parabolic Equations in Smooth Domains. <\/a>Stochastics and Stochastics Reports, Vol. 68, No. 1-2, pp. 145-175, 2000.<\/li>\n
    14. M. Huebner and S. V. Lototsky. Asymptotic Analysis of the Sieve Estimator for a Class of Parabolic SPDEs. <\/a>Scandinavian Journal of Statistics, Vol. 27, No. 2, pp. 353-370, 2000.<\/li>\n
    15. S. V. Lototsky and B. L. Rozovskii. Parameter Estimation for Stochastic Evolution Equations with Non-commuting Operators. <\/a>In: V. Korolyuk, N. Portenko, and H. Syta (editors), Skorokhod’s Ideas in Probability Theory, pp. 271-280. Institute of Mathematics of the National Academy of Sciences of Ukraine, Kiev, Ukraine, 2000.<\/li>\n
    16. S. V. Lototsky. Sobolev Spaces with Weights in Domains and Boundary Value problems for Degenerate Elliptic Equations. <\/a>Methods and Applications of Analysis, Vol.7, No. 1, pp. 195-204, 2000.<\/li>\n
    17. M. Huebner and S. V. Lototsky. Asymptotic Analysis of a Kernel Estimator for Parabolic SPDEs with Time-Dependent Coefficients. <\/a>Annals of Applied Probability, Vol. 10, No. 4, pp. 1-13, 2000.<\/li>\n
    18. S. V. Lototsky. Linear Stochastic Parabolic Equations, Degenerating at the Boundary.<\/a> Electronic Journal of Probability, Vol. 6, paper number 24, 2001.<\/li>\n
    19. S. V. Lototsky. Small perturbation of stochastic parabolic equations: a power series analysis <\/a>. Journal of Functional Analysis, Vol. 193, No. 1, pp. 94-115, 2002.<\/li>\n
    20. S. V. Lototsky. Parameter Estimation for Stochastic Parabolic Equations: Asymptotic Properties of a Two-Dimensional Projection Based Estimator.<\/a> Statistical Inference for Stochastic Processes, Vol. 6, No. 1, pp. 65-87, 2003. Also available on the journal web site.<\/a><\/li>\n
    21. S. V. Lototsky. Nonlinear Filtering of Diffusion Processes in Correlated Noise: Analysis by Separation of Variables. <\/a>Applied Mathematics and Optimization, Vol. 47, No. 2, pp. 167-194, 2003. Also, posted on the journal web site <\/a>and the archive site.<\/a><\/li>\n
    22. S. V. Lototsky. Optimal Filtering of Stochastic Parabolic Equations. <\/a>In: S. Albeverio, Z-M. Ma, and M. Roeckner (editors), Recent Developments in Stochastic Analysis and Related Topics (Proceedings of the First Sino-German Conference on Stochastic Analysis), pp. 330-353, World Scientific, 2004.<\/li>\n
    23. S. V. Lototsky and B. L. Rozovskii. Passive Scalar Equation in a Turbulent Incompressible Gaussian Velocity Field. <\/a>Russian Mathematical Surveys, Vol. 59, No. 2, pp. 297-312, 2004. See also the journal web page<\/a><\/li>\n
    24. S. V. Lototsky and B. L. Rozovskii. Stochastic Differential Equations: A Wiener Chaos Approach. <\/a>In: Yu. Kabanov, R. Liptser, and J. Stoyanov (editors), From Stochastic Calculus to Mathematical Finance: The Shiryaev Festschrift, pp. 433-507, Springer, 2006.<\/li>\n
    25. S. V. Lototsky and B. L. Rozovskii. Wiener Chaos Solutions of Linear Stochastic Evolution Equations. <\/a>Annals of Probability, Vol. 34, No. 2, pp. 638-662, 2006. See also the journal web page.<\/a><\/li>\n
    26. S. V. Lototsky. Wiener Chaos and Nonlinear Filtering. <\/a>Applied Mathematics and Optimization, Vol. 54, No. 3, pp. 265-291, 2006. On-line <\/a>(The official journal web page).<\/li>\n
    27. S. V. Lototsky. A Random Change of Variables and Applications to the Stochastic Porous Medium Equation with Multiplicative Time Noise. <\/a>Communications on Stochastic Analysis, Vol. 1, No. 3, pp. 343-355, 2007.<\/li>\n
    28. S. V. Lototsky and B. L. Rozovskii. Stochastic Parabolic Equations of Full Second Order. <\/a>IMA Vol. 145, pp. 199-210, 2007.<\/li>\n
    29. S. V. Lototsky and K. Stemmann. Solving SPDEs Driven by Colored Noise: a Chaos Approach. Quarterly of Applied Mathematics, Vol. 66, No. 3, pp. 499-520, 2008. Arxive<\/a> Journal<\/a><\/li>\n
    30. S. V. Lototsky. Statistical Inference for Stochastic Parabolic Equations: A Spectral Approach.<\/a> Publ. Mat. (Publicacions Matematiques), Vol. 53, No. 1, pp. 3\u201345, 2009.<\/li>\n
    31. S. V. Lototsky and K. Stemmann. Stochastic Integrals and Evolution Equations with Gaussian Random Fields. <\/a>Applied Mathematics and Optimization, Vol. 59, No. 2, pp. 203-232, 2009.<\/li>\n
    32. Ig. Cialenco, S. V. Lototsky, and Jan Pospisil. Asymptotic Properties of the Maximum Likelihood Estimator for Stochastic Parabolic Equations with Additive Fractional Brownian Motion. <\/a>Stochastics and Dynamics, Vol. 9, No. 2, pp. 169-185, 2009.<\/li>\n
    33. S. V. Lototsky and B. L. Rozovskii. Stochastic Differential Equations Driven by Purely Spatial Noise. <\/a>SIAM J Math. Anal., Vol. 41, No. 4, pp. 1295-1322, 2009.<\/li>\n
    34. Ig. Cialenco and S. V. Lototsky. Parameter Estimation in Diagonalizable Bilinear Stochastic Parabolic Equations. <\/a>Statistical Inference for Stochastic Processes, Vol. 12, No. 3, pp. 203-219, 2009.<\/li>\n
    35. S. V. Lototsky and B. L. Rozovskii. A Unified Approach to Stochastic Evolution Equations Using the Skorokhod Integral. <\/a>Theory of Probability and its Applications, Vol. 54, No. 2, pp. 189-202, 2010.<\/li>\n
    36. W. Liu and S. V. Lototsky. Parameter Estimation in Hyperbolic Multichannel Models. <\/a>Asymptotic Analysis, Vol. 68, No. 4, pp. 223-248, 2010.<\/li>\n
    37. S. V. Lototsky, B. L. Rozovskii, and X. Wan. Elliptic Equations of Higher Stochastic Order. <\/a>ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM:M2AN), Volume 44, No 5, pp. 1135-1153, 2010.<\/li>\n
    38. W. Liu and S. V. Lototsky. Estimating Speed and Damping in the Stochastic Wave Equation. <\/a>In: G. Da Prato and L. Tubaro (editors), Stochastic Partial Differential Equations and Applications, Quaderni di Matematica, Vol. 25, pp. 191-206. Dipartimento di Matematica, Seconda Universita di Napoli, 2010; ISBN 978-88-548-4391-2.<\/li>\n
    39. S. V. Lototsky and B. L. Rozovskii. Bilinear Stochastic Elliptic Equations. <\/a>In: G. Da Prato and L . Tubaro (editors), Stochastic Partial Differential Equations and Applications, Quaderni di Matematica, Vol. 25, pp. 207-221. Dipartimento di Matematica, Seconda Universita di Napoli, 2010; ISBN 978-88-548-4391-2.<\/li>\n
    40. S. V. Lototsky. Chaos Approach to Nonlinear Filtering. In: D. Crisan and B. L. Rozovskii (editors), The Oxford Handbook of Nonlinear Filtering, pp. 231-264, Oxford University Press, 2011.<\/li>\n
    41. N. Lin and S. V. Lototsky. Undamped Harmonic Oscillator Driven by Additive Gaussian White Noise: A Statistical Analysis. <\/a>Communications on Stochastic Analysis, Vol. 5, No. 1, pp. 233-250, 2011.<\/li>\n
    42. S. Kaligotla and S. V. Lototsky. Wick Product in The Stochastic Burgers Equation: A Curse or a Cure? <\/a>Asymptotic Analysis, Vol. 75, No 3-4, pp. 145-168, 2011.<\/li>\n
    43. S. V. Lototsky, B. L. Rozovskii and D. Sele\u0161i. On generalized Malliavin calculus. <\/a>Stochastic Processes and their Applications, Vol. 122, No. 3, pp. 808-843, 2012.<\/li>\n
    44. S. V. Lototsky and J. Zhong. Stochastic Evolution Systems With Constant Coefficients.<\/a> Stochastic Partial Differential Equations: Analysis and Computations, Vol. 1, No. 4, pp. 687-711, 2013. (First Online: November 19, 2013)<\/li>\n
    45. N. Lin and S. V. Lototsky. Second-order continuous-time non-stationary Gaussian autoregression.<\/a> Statistical Inference for Stochastic Processes, Vol. 17, No. 1, pp. 19-49, 2014.<\/li>\n
    46. S. V. Lototsky. Simple spectral bounds for sums of certain Kronecker products.<\/a> Linear Algebra and its Applications, Vol. 469, pp. 114-129, 2015.<\/li>\n
    47. S. V. Lototsky and M. Moers. Large-time and small-ball asymptotics for quadratic functionals of Gaussian diffusions.<\/a> Asymptotic Analysis, Vol. 95, No. 3-4, pp. 345-374, 2015.<\/li>\n
    48. S. V. Lototsky. Small ball probabilities for the infinite-dimensional Ornstein\u2013Uhlenbeck process in Sobolev spaces. <\/a>Stochastics and Partial Differential Equations: Analysis and Computations, Vol. 5, No. 2, pp. 192-219, 2017. (First Online: October 26, 2016)<\/li>\n
    49. H.-J. Kim and S. V. Lototsky. Time-homogeneous parabolic Wick\u2013Anderson model in one space dimension: regularity of solution. <\/a>Stochastics and Partial Differential Equations: Analysis and Computations, Vol. 5, No. 4, pp. 559-591, 2017. (First Online: May 12, 2017)<\/li>\n
    50. H.-J. Kim and S. V. Lototsky. An asymptotic comparison of two time-homogeneous PAM models. <\/a>Communications on Stochastic Analysis, Vol. 12, No. 2, pp. 185-196, 2018.<\/li>\n
    51. H.-J. Kim and S. V. Lototsky. Heat equation with a geometric rough path potential in one space dimension: existence and regularity of solution. <\/a> Communications of the Korean Mathematical Society, Vol. 34, No. 3, pp. 757-769, 2019.<\/li>\n
    52. Ig. Cialenco, H.-J. Kim and S. V. Lototsky. Statistical analysis of some evolution equations driven by space-only noise. <\/a> Statistical Inference for Stochastic Processes. (First Online: July 29, 2019)<\/li>\n
    53. S. V. Lototsky and B. L. Rozovskii. Classical and Generalized Solutions of Fractional Stochastic Differential Equations. Stochastics and Partial Differential Equations: Analysis and Computations, Vol. 8, No. 4, pp. 761-786, 2020. (First Online: December 7, 2019)<\/li>\n
    54. S. V. Lototsky and A. Shah. Gaussian fields and stochastic heat equations. Differential and Integral Equations, Vol. 33, No. 9-10, pp. 527-554, 2020.<\/li>\n
    55. S. V. Lototsky and A. Pollok. Kelly Criterion: From a Simple Random Walk to L\u00e9vy Processes. SIAM Journal on Financial Mathematics, Vol. 12, No. 1, pp. 342-368, 2021.<\/li>\n
    56. S. V. Lototsky, H. Schellhorn, and R. Zhao. An Infinite-Dimensional Model of Liquidity in Financial Markets<\/a>. Probability, Uncertainty and Quantitative Risk, Vol. 6, No. 2, pp. 117-138, 2021. (First Online: June 26, 2021)<\/li>\n
    57. S. V. Lototsky, R. Mikulevicius, and B. L. Rozovskii. Intrusive and non-intrusive chaos approximation for a two-dimensional steady state Navier\u2013Stokes system with random forcing<\/a>. Stochastics and Partial Differential Equations: Analysis and Computations, Vol. 11, No. 2, pp. 481\u2013502, 2023. (First Online: January 3, 2022)<\/li>\n
    58. S. V. Lototsky. A Sharp Rate of Convergence in the Functional Central Limit Theorem with Gaussian Input<\/a>. Journal of Stochastic Analysis, Vol. 3, No. 3, Article 5 (17 pages), 2022.<\/li>\n<\/ol>\n
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      Other Publications<\/h5>\n
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