Books
  1. B. L. Rozovsky and S. V. Lototsky. Stochastic Evolution Systems, Second Edition. Springer, 2018.
  2. S. V. Lototsky and B. L. Rozovsky. Stochastic Partial Differential Equations. Springer, 2017. At Springer At Amazon.com
  3. P. Baxendale and S. Lototsky, Editors. Stochastic Differential Equations: Theory and Applications. A volume in honor of Professor B. L. Rozovskii. Volume 2 of the series “Interdisciplinary Mathematical Sciences”. World Scientific, 2007.
  4. E. K. Blum and S. V. Lototsky. Mathematics of Physics and Engineering. World Scientific, 2006. At Amazon.com At Barnes and Noble
Papers
  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.
  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.
  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.
  4. S. V. Lototsky, C. Rao, and B. L. Rozovskii. Fast Nonlinear Filter for Continuous-Discrete Time Multiple Models, Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan, Dec. 11-13, 1996, Vol. 4, pp. 4071-4076, Omnipress, Madison, WI.
  5. S. V. Lototsky, R. Mikulevicius, and B. L. Rozovskii. Nonlinear Filtering Revisited: a Spectral Approach, II, Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan, Dec. 11-13, 1996, Vol. 4, pp. 4060-4064, Omnipress, Madison, WI.
  6. S. V. Lototsky, R. Mikulevicius, and B. L. Rozovskii. Nonlinear Filtering Revisited: a Spectral Approach , SIAM Journal on Control and Optimization, Vol. 35, No. 2, pp. 435-461, March 1997.
  7. S. V. Lototsky and B. L. Rozovskii. Recursive Multiple Wiener Integral Expansion for Nonlinear Filtering of Diffusion Processes . 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.
  8. M. Huebner, S. V. Lototsky, and B. L. Rozovskii. Asymptotic Properties of an Approximate Maximum Likelihood Estimator for Stochastic PDEs. 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.
  9. S. V. Lototsky and B. L. Rozovskii. Recursive Nonlinear Filter for a Continuous – Discrete Time Model: Separation of Parameters and Observations, IEEE Transactions on Automatic Control, Vol. 43, No. 8, pp. 1154-1158, August 1998.
  10. N. V. Krylov and S. V. Lototsky. A Sobolev Space Theory of SPDEs with Constant Coefficients on a Half Line. SIAM Journal on Mathematical Analysis. Vol. 30, No. 2, pp. 298-325, March 1999.
  11. S. V. Lototsky and B. L. Rozovskii. Spectral Asymptotics of Some Functionals Arising in Statistical Inference for SPDEs. Stochastic Processes and Their Application, Vol. 79, No. 1, pp. 69-94, 1999.
  12. N. V. Krylov and S. V. Lototsky. A Sobolev Space Theory of SPDEs with Constant Coefficients in a Half Space. SIAM Journal on Mathematical Analysis, Vol. 31, No. 1, pp. 19-33, 2000.
  13. S. V. Lototsky. Dirichlet Problem for Stochastic Parabolic Equations in Smooth Domains. Stochastics and Stochastics Reports, Vol. 68, No. 1-2, pp. 145-175, 2000.
  14. M. Huebner and S. V. Lototsky. Asymptotic Analysis of the Sieve Estimator for a Class of Parabolic SPDEs. Scandinavian Journal of Statistics, Vol. 27, No. 2, pp. 353-370, 2000.
  15. S. V. Lototsky and B. L. Rozovskii. Parameter Estimation for Stochastic Evolution Equations with Non-commuting Operators. 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.
  16. S. V. Lototsky. Sobolev Spaces with Weights in Domains and Boundary Value problems for Degenerate Elliptic Equations. Methods and Applications of Analysis, Vol.7, No. 1, pp. 195-204, 2000.
  17. M. Huebner and S. V. Lototsky. Asymptotic Analysis of a Kernel Estimator for Parabolic SPDEs with Time-Dependent Coefficients. Annals of Applied Probability, Vol. 10, No. 4, pp. 1-13, 2000.
  18. S. V. Lototsky. Linear Stochastic Parabolic Equations, Degenerating at the Boundary. Electronic Journal of Probability, Vol. 6, paper number 24, 2001.
  19. S. V. Lototsky. Small perturbation of stochastic parabolic equations: a power series analysis . Journal of Functional Analysis, Vol. 193, No. 1, pp. 94-115, 2002.
  20. S. V. Lototsky. Parameter Estimation for Stochastic Parabolic Equations: Asymptotic Properties of a Two-Dimensional Projection Based Estimator. Statistical Inference for Stochastic Processes, Vol. 6, No. 1, pp. 65-87, 2003. Also available on the journal web site.
  21. S. V. Lototsky. Nonlinear Filtering of Diffusion Processes in Correlated Noise: Analysis by Separation of Variables. Applied Mathematics and Optimization, Vol. 47, No. 2, pp. 167-194, 2003. Also, posted on the journal web site and the archive site.
  22. S. V. Lototsky. Optimal Filtering of Stochastic Parabolic Equations. 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.
  23. S. V. Lototsky and B. L. Rozovskii. Passive Scalar Equation in a Turbulent Incompressible Gaussian Velocity Field. Russian Mathematical Surveys, Vol. 59, No. 2, pp. 297-312, 2004. See also the journal web page
  24. S. V. Lototsky and B. L. Rozovskii. Stochastic Differential Equations: A Wiener Chaos Approach. In: Yu. Kabanov, R. Liptser, and J. Stoyanov (editors), From Stochastic Calculus to Mathematical Finance: The Shiryaev Festschrift, pp. 433-507, Springer, 2006.
  25. S. V. Lototsky and B. L. Rozovskii. Wiener Chaos Solutions of Linear Stochastic Evolution Equations. Annals of Probability, Vol. 34, No. 2, pp. 638-662, 2006. See also the journal web page.
  26. S. V. Lototsky. Wiener Chaos and Nonlinear Filtering. Applied Mathematics and Optimization, Vol. 54, No. 3, pp. 265-291, 2006. On-line (The official journal web page).
  27. S. V. Lototsky. A Random Change of Variables and Applications to the Stochastic Porous Medium Equation with Multiplicative Time Noise. Communications on Stochastic Analysis, Vol. 1, No. 3, pp. 343-355, 2007.
  28. S. V. Lototsky and B. L. Rozovskii. Stochastic Parabolic Equations of Full Second Order. IMA Vol. 145, pp. 199-210, 2007.
  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 Journal
  30. S. V. Lototsky. Statistical Inference for Stochastic Parabolic Equations: A Spectral Approach. Publ. Mat. (Publicacions Matematiques), Vol. 53, No. 1, pp. 3–45, 2009.
  31. S. V. Lototsky and K. Stemmann. Stochastic Integrals and Evolution Equations with Gaussian Random Fields. Applied Mathematics and Optimization, Vol. 59, No. 2, pp. 203-232, 2009.
  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. Stochastics and Dynamics, Vol. 9, No. 2, pp. 169-185, 2009.
  33. S. V. Lototsky and B. L. Rozovskii. Stochastic Differential Equations Driven by Purely Spatial Noise. SIAM J Math. Anal., Vol. 41, No. 4, pp. 1295-1322, 2009.
  34. Ig. Cialenco and S. V. Lototsky. Parameter Estimation in Diagonalizable Bilinear Stochastic Parabolic Equations. Statistical Inference for Stochastic Processes, Vol. 12, No. 3, pp. 203-219, 2009.
  35. S. V. Lototsky and B. L. Rozovskii. A Unified Approach to Stochastic Evolution Equations Using the Skorokhod Integral. Theory of Probability and its Applications, Vol. 54, No. 2, pp. 189-202, 2010.
  36. W. Liu and S. V. Lototsky. Parameter Estimation in Hyperbolic Multichannel Models. Asymptotic Analysis, Vol. 68, No. 4, pp. 223-248, 2010.
  37. S. V. Lototsky, B. L. Rozovskii, and X. Wan. Elliptic Equations of Higher Stochastic Order. ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM:M2AN), Volume 44, No 5, pp. 1135-1153, 2010.
  38. W. Liu and S. V. Lototsky. Estimating Speed and Damping in the Stochastic Wave Equation. 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.
  39. S. V. Lototsky and B. L. Rozovskii. Bilinear Stochastic Elliptic Equations. 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.
  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.
  41. N. Lin and S. V. Lototsky. Undamped Harmonic Oscillator Driven by Additive Gaussian White Noise: A Statistical Analysis. Communications on Stochastic Analysis, Vol. 5, No. 1, pp. 233-250, 2011.
  42. S. Kaligotla and S. V. Lototsky. Wick Product in The Stochastic Burgers Equation: A Curse or a Cure? Asymptotic Analysis, Vol. 75, No 3-4, pp. 145-168, 2011.
  43. S. V. Lototsky, B. L. Rozovskii and D. Seleši. On generalized Malliavin calculus. Stochastic Processes and their Applications, Vol. 122, No. 3, pp. 808-843, 2012.
  44. S. V. Lototsky and J. Zhong. Stochastic Evolution Systems With Constant Coefficients. Stochastic Partial Differential Equations: Analysis and Computations, Vol. 1, No. 4, pp. 687-711, 2013. (First Online: November 19, 2013)
  45. N. Lin and S. V. Lototsky. Second-order continuous-time non-stationary Gaussian autoregression. Statistical Inference for Stochastic Processes, Vol. 17, No. 1, pp. 19-49, 2014.
  46. S. V. Lototsky. Simple spectral bounds for sums of certain Kronecker products. Linear Algebra and its Applications, Vol. 469, pp. 114-129, 2015.
  47. S. V. Lototsky and M. Moers. Large-time and small-ball asymptotics for quadratic functionals of Gaussian diffusions. Asymptotic Analysis, Vol. 95, No. 3-4, pp. 345-374, 2015.
  48. S. V. Lototsky. Small ball probabilities for the infinite-dimensional Ornstein–Uhlenbeck process in Sobolev spaces. Stochastics and Partial Differential Equations: Analysis and Computations, Vol. 5, No. 2, pp. 192-219, 2017. (First Online: October 26, 2016)
  49. H.-J. Kim and S. V. Lototsky. Time-homogeneous parabolic Wick–Anderson model in one space dimension: regularity of solution. Stochastics and Partial Differential Equations: Analysis and Computations, Vol. 5, No. 4, pp. 559-591, 2017. (First Online: May 12, 2017)
  50. H.-J. Kim and S. V. Lototsky. An asymptotic comparison of two time-homogeneous PAM models. Communications on Stochastic Analysis, Vol. 12, No. 2, pp. 185-196, 2018.
  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. Communications of the Korean Mathematical Society, Vol. 34, No. 3, pp. 757-769, 2019.
  52. Ig. Cialenco, H.-J. Kim and S. V. Lototsky. Statistical analysis of some evolution equations driven by space-only noise. Statistical Inference for Stochastic Processes. (First Online: July 29, 2019)
  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)
  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.
  55. S. V. Lototsky and A. Pollok. Kelly Criterion: From a Simple Random Walk to Lévy Processes. SIAM Journal on Financial Mathematics, Vol. 12, No. 1, pp. 342-368, 2021.
  56. S. V. Lototsky, H. Schellhorn, and R. Zhao. An Infinite-Dimensional Model of Liquidity in Financial Markets. Probability, Uncertainty and Quantitative Risk, Vol. 6, No. 2, pp. 117-138, 2021. (First Online: June 26, 2021)
  57. S. V. Lototsky, R. Mikulevicius, and B. L. Rozovskii. Intrusive and non-intrusive chaos approximation for a two-dimensional steady state Navier–Stokes system with random forcing. Stochastics and Partial Differential Equations: Analysis and Computations, Vol. 11, No. 2, pp. 481–502, 2023. (First Online: January 3, 2022)
  58. S. V. Lototsky. A Sharp Rate of Convergence in the Functional Central Limit Theorem with Gaussian Input. Journal of Stochastic Analysis, Vol. 3, No. 3, Article 5 (17 pages), 2022.
Other Publications