Boris Rozovsky, Publications

Books:

Stochastic Partial Differential Equations (with S. Lototsky), Springer (to appear).

Stochastic evolution systems.  Linear theory and applications to the statistics of random processes (in Russian).  Moscow: “Nauka,” 1983.

Data analysis in chemical research.  Statistical foundations (in Russian). Moscow: “Khimija,” 1984.

Stochastic evolution systems.  Linear theory with applications to non-linear filtering.  Mathematics and its Applications (Soviet Series) 35.  Dordrecht: Kluwer Academic Publishers, 1990.

Stochastic Navier-Stokes equations: a Wiener chaos approach (with R. Mikulevicius).  Applications of Mathematics Series.  Springer-Verlag, forthcoming.

Edited Volumes:

Handbook on Nonlinear Filtering, (Ed. D. Crisan and B. Rozovskii) Oxford University Press (to appear in 2008).

Applied Mathematics & Optimization. Special issue on Approximation in Stochastic Partial Differential Equations, (Guest Ed. B. Rozovskii), Springer, 2006.

Stochastic partial differential equations: six perspectives.  (Ed. R. Carmona and B. L. Rozovskii)  Mathematical Surveys and Monographs Series 64.  Providence, RI: American Mathematical Society, 1998.

Statistics and control of stochastic processes.  The Liptser festschrift: papers from the Steklov Seminar (Moscow, 1995/1996).  Ed. Yu. M. Kabanov, B. L. Rozovskii, and A. N. Shiryaev.  River Edge, NJ: World Scientific, 1997.

Stochastic modeling  in oceanography.  Ed. R. Adler, P. Muller, and B. L. Rozovskii.  Progress in Probability 39.  Boston: Birkhauser, 1996.

Stochastic partial differential equations and their applications.  Proceedings of the IFIP WG 7/1 International Conference (Charlotte, NC, 1991).  Ed. B. L. Rozovskii and R. B. Sowers.  Lecture Notes in Control and Information Sci. 176.  Berlin: Springer-Verlag, 1992.

Papers (in refereed journals/books)

A Unified Approach to Stochastic Evolution Equations Using the Skorokhod Integral, (with S. Lototsky), submitted.

Stochastic Differential Equations Driven by Purely Spatial Noise, (with S. Lototsky), submitted.

Stochastic parabolic equations of full second order (with S. Lototsky). Book chapter in " Topics in Stochastic Analysis and Nonparametric Estimation " (Ed. P.- L. Chow et al.). 199--210, The IMA Volumes in Mathematics and its Applications, Springer,  2007.

Wiener chaos solutions of linear stochastic evolution equations (with S. Lototsky). Annals. of  Prob., 34 (2006), no. 2, 638--662.

Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics (with T. How et al.), J. Comput. Phys. 216 (2006), no. 2, 687-706.

Stochastic differential equations: A Wiener chaos approach (with S. Lototsky). Book chapter in " From Stochastic Calculus to Mathematical Finance " (Ed. Y. Kabanov et al.). 433--506, Springer, Berlin, 2006

Strong solutions of stochastic generalized porous media equations: Existence, uniqueness and ergodicity. (with G. Da Prato et al.) Comm. Partial Dif. Eq., 31 (2006), no. 1-3, 277-291.

A novel approach to detection of intrusions in computer networks via adaptive sequential and batch-sequential change-point detection methods (with R. Blazek et al.), IEEE Transactions on Signal Processing, 54, (2006) no. 9, 3372--3382.

Sequential change-point detection methods with applications to rapid detection of intrusions in information systems (with A. Tartakovsky et al.), Statistical Methodology, to appear.

A filtering approach to tracking volatility from prices observed at random times (with J. Cvitanic et al). Annals of Applied Prob, 16 (2006), no. 3, 1633-1652.

Numerical estimation of volatility values from discretely observed diffusion data. (with J. Cvitanic and Il. Zalyapin) J. Comp. Finance, 9 (2006), no. 4,1-36.

Global L2-solutions of stochastic Navier-Stokes equations (with R. Mikulevicius). Annals of Prob., 33 (2005), No. 1, 137-176.

Passive Scalar Equation in a Turbulent Incompressible Gaussian Velocity Field (with S. Lototsky), Rus. Mat. Surv. 59 (2004), No.2,

Stochastic Navier-Stokes equations for turbulent flows (with R. Mikulevicius). SIAM J. Math. Anal.  35 (2004), No. 5, 1250-1310.

A diffusion model of roundtrip time (with S. Bohacek).  Computational Statistics and Data Analysis, Computational Statistics and Data Analysis, vol. 45 (2004) no. 1, 25-50.

On martingale problem solutions for stochastic Navier-Stokes equations (with R. Mikulevicius).  In Stochastic partial differential equations and applications, ed. G. Da Prato and L. Tubaro. Lecture Notes in Pure and Applied Mathematics Series 227.  New York: Marcel Dekker, 2002.

A note on Krylov's -theory for systems of SPDEs (with R. Mikulevicius).  Electron. J. Probab. 6, no. 12 (2001): 1–35.

On equations of stochastic fluid mechanics (with R. Mikulevicius).  In Stochastics in finite and infinite dimensions: in honor of Gopinath Kallianpur, ed. T. Hida et al., 285–302.  Trends Math.  Boston: Birkhauser, 2001. 

Stochastic Navier-Stokes equations: propagation of chaos and statistical moments (with R. Mikulevicius).  In Optimal control and partial differential equations: in honor of Professor Alain Bensoussan, ed. J. L. Menaldi et al., 258–267.  Amsterdam: IOS Press, 2001.

Approximation of the Kushner equation of nonlinear filtering (with K. Ito).  SIAM J. Control Optim. 38, no. 3 (2000): 893–915. 

Parameter estimation for stochastic evolution equations with non-commuting operators (with S. Lototsky).  In Skorokhod's ideas in probability theory, ed. V. Korolyuk, N. Portenko, and H. Syta, 271–280.  Kiev: Institute of Mathematics of the National Academy of Sciences of Ukraine, 2000. 

Fourier-Hermite expansions for nonlinear filtering (with R. Mikulevicius).  Teor. Veroyatnost. i Primenen. 44, no. 3 (1999): 675–680.  Translation in Theory Probab. Appl. 44, no. 3 (2000): 606–612. 

Spectral asymptotics of some functionals arising in statistical inference for SPDE’s (with S. Lototsky).  Stochastic Process. Appl. 79, no. 1 (1999): 69–94. 

Recursive nonlinear filter for a continuous-discrete time model (with S. Lototsky).  IEEE Trans. Automatic Cont. 48, no. 8 (1998): 1154–58. 

Martingale problems for stochastic PDE's (with R. Mikulevicius).  In  Stochastic partial differential equations: six perspectives, ed. R. Carmona and B. L. Rozovskii, 243–325.  Mathematical Surveys and Monographs Series 64.  Providence, RI: American Mathematical Society, 1998.

Normalized stochastic integrals in topological vector spaces (with R. Mikulevicius).  In S3/4minaire de Probabilit3/4s XXXII, 137–165.  Lecture Notes in Math. 1686.  Berlin: Springer-Verlag, 1998. 

Linear parabolic stochastic PDE's and Wiener chaos (with R. Mikulevicius).  SIAM J. Math. Anal. 29, no. 2 (1998): 452–480.  

Weighted stochastic Sobolev spaces and bilinear SPDE's driven by space-time white noise (with D. Nualart).  J. Funct. Anal. 149, no. 1 (1997): 200–225.  

On asymptotic problems of parameter estimation in stochastic PDE's: discrete time sampling (with L. Piterbarg).  Math. Methods Statist. 6, no. 2 (1997): 200–223. 

Nonlinear filtering revisited: a spectral approach (with S. Lototsky and R. Mikulevicius).  SIAM J. Control Optim. 35, no. 2 (1997): 435–461.  

On asymptotic properties of an approximate maximum likelihood estimator for stochastic PDEs (with M. Huebner and S. Lototsky).  In Statistics and control of stochastic processes.  The Liptser festschrift: papers from the Steklov Seminar (Moscow, 1995/1996), ed. Yu. M. Kabanov, B. L. Rozovskii, and A. N. Shiryaev,  139–155.  River Edge, NJ: World Scientific, 1997.  

Recursive multiple Wiener integral expansion for nonlinear filtering of diffusion processes (with S. Lototsky).  In Stochastic processes and functional analysis, ed. J. Goldstein et al., 199–208.  Lecture Notes in Pure and App. Math 186.  New York: Marcel Dekker, 1997. 

Maximum likelihood estimators in the equations of physical oceanography (with L. Piterbarg).  In Stochastic modelling in oceanography, ed. R. Adler et al., 397–421.  Progress in Probability 39.  Boston: Birkhauser, 1996.  

On asymptotic properties of maximum likelihood estimators for parabolic stochastic PDE's (with M. Huebner).  Probab. Theory Related Fields 103, no. 2 (1995): 143–163.  

On stochastic integrals in topological vector spaces (with R. Mikulevicius). Stochastic analysis (Ithaca, NY, 1993), 593–602.  Proc. Sympos. Pure Math. 57.  Providence, RI: American Mathematics Society, 1995.  

Estimates of turbulent parameters from Lagrangian data using a stochastic particle model (with A. Griffa et al.).  Journal of Mar. Res. 53, no. 3 (1995): 371–401.

Statistics and physical oceanography (with A. Griffa et al.).  Stat. Sci. 9, no. 2 (1994): 167–201.  

Uniqueness and absolute continuity of weak solutions for parabolic SPDE's (with R. Mikulevicius).  Acta Appl. Math. 35, no. 1-2 (1994): 179–192.  

Soft solutions of linear parabolic SPDE's and the Wiener chaos expansion (with R. Mikulevicius).  In Stochastic analysis on infinite-dimensional spaces, ed. H. Kunita and H.-H. Kuo, 211–220.  Pitman Res. Notes Math. Ser. 310.  Baton Rouge, LA: Longman Sci. Tech, Harlow, 1994.  

Kinematic dynamo and intermittence in a turbulent flow.  Magnetohydrodynamic stability and dynamos (with P. Baxendale).  Geophys. Astrophys. Fluid Dynam. 73, no. 1-4 (1993): 33–60.  

Two examples of parameter estimation for stochastic partial differential equations (with M. Huebner and R. Khasminskii).  In Stochastic processes. A festschrift in honor of Gopinath Kallianpur, 149–160.  New York: Springer-Verlag, 1993. 

Some results on a diffusion approximation to the induction equation.  In Stochastic partial differential equations and applications (Trento, 1990), ed. G. Da Prato and L. Tubaro, 268–81.  Pitman Res. Notes in Math. Ser. 268.  Baton Rouge, LA: Longman Sci. Tech, Harlow, 1992.  

A simple proof of uniqueness for Kushner and Zakai equations.  In Stochastic analysis, ed. E. Mayer-Wolf, 449–58.  Boston: Academic Press, 1991.  

Measure-valued solutions of  second-order stochastic parabolic equations (with O.G. Purtukhiya) (in Russian).  In Statistics and control of random processes, ed. A. N. Shiryaev, 177–79.  Moscow: “Nauka,” 1989.  

On the mathematical theory of a hydromagnetic dynamo in a random flow (in Russian).  Dokl. Akad. Nauk SSSR 293, no. 6 (1987): 1311–1314.  

On the statistic estimation of reliability of determining aqueous solution pH by acid-base indicator paper (with V.M. Ostrovskaja et al.) (in Russian).  J. of Analit. Chem. USSR Acad. of Sci. V(XLII), 1987.  

Nonnegative L­_{1}-solutions of second order stochastic parabolic equations with random coefficients.  In Statistics and control of stochastic processes:papers from the Steklov Seminar (Moscow, 1984), ed. N. V. Krylov, R. S. Liptser, and A. A. Novikov, 410–427.  Translation Series in Math and Engineering.  New York: Optimization Software, 1985.  

Filtering interpolation and extrapolation of degenerate diffusion processes. Backward equations (in Russian). Teor. Veroyatnost. i Primenen 28, no. 4 (1983): 725–737.  

Stochastic partial differential equations and diffusion processes (with N. V. Krylov)(in Russian).  Uspekhi Mat. Nauk 37, no. 6 (1982): 75–95.  

Characteristics of second-order degenerate parabolic Ito equations (with N. V. Krylov)(in Russian).  Trudy Sem. Petrovsk. 8 (1982): 153–168.  

Smoothness of solutions of stochastic evolution equations and the existence of a filtering transition density (with A. Shimizu).  Nagoya Math. J. 84 (1981): 195–208.  

On the first integrals and Liouville equations for diffusion processes (with N. V. Krylov).  In Stochastic differential systems (Visegrad, 1980), 117–125.  Lecture Notes in Control and Information Sci. 36.  New York: Springer-Verlag, 1981.  

On the total integral of Ito equations (with N.V. Krylov).  Russian Math. Surveys (UMN) 4: 1980.  

A note on the strong solutions of stochastic differential equations with random coefficients.  In Stochastic differential systems. Proceedings of the IFIP-WG 7/1 Working Conference (Vilnius, Lithuania, 1978), 287–296.  Lecture Notes in Control and Information Sci. 25.  New York: Springer-Verlag, 1980.  

Conditional distributions of degenerate diffusion processes (in Russian).  Teor. Veroyatnost. i Primenen. 25, no. 1 (1980): 149–154.  

Ito equations in Banach spaces and strongly parabolic stochastic partial differential equations (with N. V. Krylov)(in Russian).  Dokl. Akad. Nauk SSSR 249, no. 2 (1979): 285–289.  

Stochastic evolution equations (with N. V. Krylov)(in Russian), 71–147.  Current Problems in Mathematics 14, 71–147.  Moscow: Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii, 1979.  

Fundamental solutions of stochastic partial differential equations and the filtering of diffusion processes (with L. G. Margulis)(in Russian).  Uspekhi Mat. Nauk 33, no. 2 (1978): 197.  

Conditional distributions of diffusion processes (with N. V. Krylov)(in Russian).  Izv. Akad. Nauk SSR Ser. Mat. 42, no. 2 (1978): 356–378.  

The Cauchy problem for linear stochastic partial differential equations (with N. V. Krylov)(in Russian).  Izv. Akad. Nauk SSR Ser. Mat. 41, no. 6 (1977): 1329–1347.

Stochastic partial differential equations (in Russian).  (Mat. Sb. (N.S.)) 96, no. 138 (1975): 314–341.  

Stochastic differential equations in infinite-dimensional spaces and filtering problems (in Russian).  In Proceedings of the School and Seminar on the Theory of Random Processes (Druskininkai, 1974), Part II, 147–194.  Vilnius: Inst. Fiz. i Mat. Akad. Nauk Litovsk. SSR, 1975.  

The Ito-Wentzell formula (in Russian).  Vestnik Moskov. Univ. Ser. i Mat. Meh. 28, no.1 (1973): 26–32.  

On infinite systems of stochastic differential equations that arise in the theory of optimal nonlinear filtering (with A.N. Shiryaev) (in Russian).  Teor. Verojatnost. i Primenen. 17 (1972): 228–237.  

Stochastic partial differential equations that arise in nonlinear filtering problems (in Russian).  Uspekhi Mat. Nauk 27, no. 3 (1972): 213–214.  

The problem of ''disorder'' for a Poisson process (with L. I. Galtchuk) (in Russian).  Teor. Verojatnost. i Primenen. 16 (1971): 729–734.