Boris L. Rozovsky Center For Applied Mathematical Sciences Department of Mathematics University of Southern California Los Angeles, CA 90089-1113

4.      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)

1.      Efficient Nonlinear Filtering Methods for Detection of Dim Targets by Passive Systems (with A. Petrov et al.)

Multitarget-Multisensor Tracking: Applications and Advances, Volume IV, 2004,   submitted.

 

2.      Stochastic Navier-Stokes equations for turbulent flows (with R. Mikulevicius). SIAM J. Math. Anal. , forthcoming.

3.      Global L₂-solutions of stochastic Navier-Stokes equations (with R. Mikulevicius). Annals of Prob. , forthcoming

4.      Wiener Chaos expansions and numerical solutuions of randomly forced equations of fluid dynamics (with T. How et al.), forthcoming.

5.      A diffusion model of roundtrip time (with S. Bohacek).  Computational Statistics and Data Analysis, forthcoming.

6.      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.

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

8.      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. 

9.      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.

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

11.  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.

12.  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.

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

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

15.  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.

16.  Normalized stochastic integrals in topological vector spaces (with R. Mikulevicius).  In S¾minaire de Probabilit¾s XXXII, 137�165.  Lecture Notes in Math. 1686.  Berlin: Springer-Verlag, 1998.

17.  Linear parabolic stochastic PDE's and Wiener chaos (with R. Mikulevicius).  SIAM J. Math. Anal. 29, no. 2 (1998): 452�80.

18.  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.

19.  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.

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

21.  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.

22.  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.

23.  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.

24.  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.

25.  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.

26.  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.

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

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

29.  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.

30.  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.

31.  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.

32.  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.

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

34.  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.

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

36.  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.

37.  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.

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

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

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

41.  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.

42.  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.

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

44.  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.

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

46.  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.

47.  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.

48.  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.

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

50.  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.

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

52.  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.

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

54.  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.

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

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

57.  Tracking volatility (with J. Cvitanic and R. Liptser). In preparation.

58.  Numerical methods for SPDEs: A Wiener chaos approach (with T. How et al.). In preparation.

59.  Weak solutions of stochastic Navier-Stokes equations (with R. Mikulevicius). In preparation.

60.  Stochastic projections. Analysis and numerical applications (with S. Lototsky). In Preparation.

Selected Conference Proceedings

1.      The quickest sequential detection of intrusions in computer networks (with R. Blazek, H. Kim, and A.Tartakovsky) In Proceedings of Interface 2003 (forthcoming).

2.       A Novel Approach to Detection of ``Denial-of-Service'' Attacks via Adaptive Sequential and Batch-Sequential Change-Point Detection Methods (with R. Blazek, H. Kim, and A.Tartakovsky).  In Proceedings of the 2nd Annual IEEE Systems, Man, and Cybernetics Information Assurance Workshop (West Point, NY, 2001).  New York: Institute of Electrical and Electronics Engineers, 2001.

3.      A New Adaptive Batch and Sequential Methods for Rapid Detection of Network Traffic Changes with Emphasis on Detection of ''Denial-of-Service'' Attacks, (with R. Blazek, H. Kim).  In Proceedings of the 53rd Session of the International Statistical Institute ( Seoul, 2001).  New York: Physica-Verlag, 2001.

4.      Tracking Volatility (with J. Cvitanic and R. Liptser).  In Proceedings of the 39th IEEE Conference on Decision and Control, IEEE Control Systems Society (Sydney, 2000).  New York: Institute of Electrical and Electronics Engineers, 2000.

5.       Interactive Banks of Bayesian Matched Filters (with R. Blazek and A. Petrov).  In SPIE Proceedings (Vol. 4048): Signal and Data Processing of Small Targets (Orlando, FL, 2000), ed. O. E. Drummond.  Bellingham, WA: SPIE (The International Society for Optical Engineering), 2000.

6.      Optimal nonlinear filtering for track-before-detect in IR image sequences (with A. Petrov).  In SPIE Proceedings (Vol. 3809): Signal and Data Processing of Small Targets (Denver, CO, 1999), ed. O. E. Drummond.  Bellingham, WA: SPIE (The International Society of Optical Engineering), 1999.

7.      An adaptive Bayesian approach to fusion of imaging and kinematic data  (with A.Tartakovsky and G.Yaralov). In Proceedings of the 2nd International Conference on Information Fusion—Fusion ’99 (Sunnyvale, CA,1999).  Madison, WI: Omnipress, 1999.

8.      Matched filters and hidden Markov models with distributed observation (with S. Kligys).  In Proceedings of the Fourth Annual U.S. Army Conference on Applied Statistics (Aberdeen Proving Ground, MD, 1998), ed. Barry A. Bodt.  ARL-SR-84.  Aberdeen, MD: Army Research Laboratory, 1999.

9.      State estimation in hidden Markov models with distributed observation (with S. Kligys).  In Theory and Practice of Control Systems: Proceedings of the 6th IEEE Mediterranean Conference (Alghero, Sardinia, 1998), ed. A. Tornambe et al.  River Edge, NJ: World Scientific, 1998.

10.  Splitting-up discretization for Kushner’s equation of nonlinear filtering (with K. Ito).  In Proceedings of the 36th IEEE Conference on Decision and Control, IEEE Control Systems Society (San Diego, CA, 1997).  New York: Institute of Electrical and Electronics Engineers, 1998.

11.  Solving hidden Markov problems by spectral approach (with C.P. Fung).  In Proceedings of the 3rd IEEE Mediterranean Symposium, Vol. II (PLACE, 1995). New York: Institute of Electrical and Electronics Engineers, 1995.

12.  Separation of observations and parameters in nonlinear filtering (with R. Mikulevicius).  Proceedings of the 32nd IEEE Conference on Decision and Control, Vol. 2, IEEE Control Systems Society (San Antonio, TX, 1993).  New York: Institute of Electrical and Electronics Engineers, 1993.

13.  Statistics and physical oceanography (with A. Griffa et al.).  Report of the National Research Council.  Washington, D.C.: National Academy Press, 1993.

14.  Nonlinear filtering revisited: A spectral approach II (with S. Lototsky).  Proceedings of the IEEE & SIAM CDC 35th Conference on Decision and Control, Vol. 4 (Kobe, Japan, 1996 ).  Madison, WI: Omnipress, 1997.

15.  On the kinematic dynamo problem in a random flow.  In Probability Theory and Mathematical Statistics: Proceedings of 5th Vilnius Conference on Probabilty Theory and Mathematical Statistics, Vol. II (Vilnius, Lithuania, 1985).  Utrecht: VNU Science Press, 1987.

16.  On the kinematic dynamo problem in a random flow.  In Probability Theory and Mathematical Statistics: Proceedings of the 4th Vilnius International Conference on Probability Theory and Mathematical Statistics (Vilnius, Lithuania, 1985).  Vilnius: Akad. Nauk Litovsk. SSR, Inst. Mat. i Kibernet, 1985.

17.  Filtering of degenerate diffusion type processes. Backward equations. In Stochastic Optimization International Conf. Abstracts, Part II (Kiev,1984

18.  Backward equations of conditional and unconditional diffusion.  In Proceedings of the 4th Soviet-Japan Symp. on Probab. Theor. and Math. Stat. Abstracts (Tbilisi, 1982).

19.  Backward filtering equations.  In 15th All-Union School-Colloquium on Probab. Theor. And Math. Stat. Abstracts (Bakuriani, 1981).  Tbilisi: “Metsniereba,” 1981.

20.  Liouville equations for a diffusion Markov process (in Russian). In 14th All Union School on Probab. Theor. and Math. Stat. Abstracts (Bakuriani, 1980).  Tbilisi: “Metsniereba,” 1980.

21.  On the first integral and Liouville equations.  In Abstracts of 3^rd Working  Conference on Stochastic Differential Equations (Visegrad, 1980), Budapest, SZAMKI, 1980.

22.  On the extrapolation of a signal with a martingale type noise (in Russian).  In 5th International Symposium on Inform. Theory Abstracts (Tbilisi,1979). [publisher? year of conference same as year of pub?]

23.  Non-linear filtering of diffusion processes: an analytical approach.  In International Symposium on Stochastic Differential Equations.  Abstracts of Communications (Vilnius, 1978).  Vilnius: Inst. Math. and Cybernet. Acad. Sci. Lithuanian SSR, 1978.

24.  On Ito equations in Hilbert spaces.  In 2nd Vilnius Conference on Probability and Mathematical Statistics. Abstracts of Communications (Vilnius, 1977).  Vilnius: Inst. Mat. i Kibernet. Akad. Nauk Litovsk. SSR, 1977.

25.  On Cauchy problem for superparabolic stochastic differential equations (with N.V. Krylov).  In Proceedings of the Third Japan-USSR Symposium on Probability Theory (Tashkent, 1975).  Lecture Notes in Mathematics 550.  New York: Springer-Verlag, 1976.

26.  On stochastic differential equations in partial derivatives.  In International Conference on Probability Theory and Mathematical Statistics.  Abstracts of Communications (Vilnius, 1973).  Vilnius: Akad. Nauk Litovsk. SSR, 1973.

27.  Reduced form of non-linear filtering equations (with A.N. Shiryaev).  In IFAC Symposium on Stochastic Control.  Supplement of abstracts (Budapest, 1974). 

Selected Technical Reports and Teaching Aids

1.      Stochastic Navier-Stokes equations for turbulent flows (with R. Mikulevicius).  WarwickPreprint: 21/ 2001.

2.       Detection algorithms and track-before-detect architecture based on nonlinear filtering for infrared search and track systems (with S. Kligys and A. Tartakovsky).  Technical Report CAMS-98.9.1, Center for Applied Mathematical Sciences, University of Southern California, 1998.

3.      Domain pursuit method for tracking ballistic targets (with R. Rao and A.Tartakovsky).  Technical Report CAMS-98.9.2, Center for Applied Mathematical Sciences, University of Southern California, 1998.

4.      Parameter estimation for stochastic evolution equations with non-commuting operators (with S. V. Lototsky). IMA Preprint Series #1501,  University of Minnesota, 1997.

5.      Statistics and physical oceanography (with A. Griffa et al.).  Report of the National Research Council, National Academy Press, 1993.

6.      Lecture notes on stochastic partial differential equations. University of North Carolina, Charlotte, 1990.

7.      Real time statistical quality control (with Yu. P. Adler)(in Russian).  Znanije Publishing House, Moscow, 1984.

8.      Studies in the theory of stochastic partial differential equations (in Russian). Doctor of Sci. Dissertation (Vilnius, Lithuania, 1984).

9.      Statistical methods in chemical industry. Methods and instructions (with B. I. Pashko et al.)(in Russian).  Center for Scientific Organization of Labor in Chemistry, Moscow 1983.

10.  Mathematical design of experiments in textile industry (with Yu. P. Adler et al.) (in Russian).  MIASCME, 1984.

11.  Mathematics design of experiments.  Methods and instructions (with Yu. P. Adler  et al.)(in Russian).  MIASCME, 1983.

12.  Statistical methods in analytical chemistry.  Instructions (with Yu. P. Alder et al.)(in Russian).  MIASCME, 1981.

13.  Statistical quality control.  Methods and instructions (with Yu. P. Alder et al.)(in Russian).  MIASCME, 1978.

14.  Optimal design of experiments.  Methods (with Yu. P. Alder et al.)(in Russian).  MIASCME, 1978.

15.  Lectures in probability theory (in Russian).  MIASCME, 1974.

16.  On stochastic equations arising in filtering of Markov processes (in Russian).  Ph. D. Dissertation, Moscow State (Lomonosov) University, 1972

Works Available Electronically

Mathematics :

• On Equations of Stochastic Fluid Mechanics
• Weighted Stochastic Sobolev Spaces and Bilinear SPDE's Driven by Space-time White Noise
• Normalized Stochastic Integrals in Topological Vector Spaces
• Linear Parabolic Stochastic PDE's and Wiener Chaos
• Recursive Multiple Wiener Integral Expansion for Nonlinear Filtering of Diffusion Processes
• Nonlinear Filtering Revisited: A Spectral Approach
• On asymptotic problems of parameter estimation in stochastic PDE's : the case of discrete time sampling
• Recursive Nonlinear Filter for a Continuous-Discrete Time Model : Separation of Parameters and Observations
• Fast Nonlinear Filter for Continuous-Discrete Time Multiple Models*
• Martingale Problems for Stochastic PDE's
• Spectral Asymptotics of some Functionals Arising in Statistical Inference for SPDEs"
• Optimal Nonlinear Filtering for track-before-detect in IR Image Sequences
• Stochastic Navier-Stokes Equations. Propagation of Chaos and Statistical Moments
• Stochastic Evolution Systems, Kluwer Academic Publ., 1990 :

List of Misprints.