Andrew Browder

Professor of Mathematics (Emeritis)

HISTORICAL REMEMBRANCES
Geometric Measure Theory at Brown in the 1960s

CONTACT INFO
Fax: (401) 863-9013
Email: Wendell_Fleming<at>brown.edu

Mathematics Department
Box 1917
Brown University
Providence, RI 02912

COURSE SCHEDULE

Retired

RESEARCH INTERESTS

Applied Probability

BACKGROUND

RECENT PUBLICATIONS

Risk-sensitive control and an optimal investment model. INFORMS Applied Probability Conference (Ulm, 1999). Math. Finance 10 (2000), no. 2, 197--213. w/Sheu, S. J.

Deterministic and stochastic approaches to nonlinear filtering. System theory: modeling, analysis and control (Cambridge, MA, 1999), 121--129, Kluwer Internat. Ser. Engrg. Comput. Sci., 518, Kluwer Acad. Publ., Boston, MA, 2000.

A max-plus-based algorithm for a Hamilton-Jacobi-Bellman equation of nonlinear filtering. SIAM J. Control Optim. 38 (2000), no. 3, 683--710 (electronic). w/McEneaney, William M.

Optimal long term growth rate of expected utility of wealth. Ann. Appl. Probab. 9 (1999), no. 3, 871--903. w/Sheu, Shuenn-Jyi

Controlled Markov processes and mathematical finance. Nonlinear analysis, differential equations and control (Montreal, QC, 1998), 407--446, NATO Sci. Ser. C Math. Phys. Sci., 528, Kluwer Acad. Publ., Dordrecht, 1999.

Risk-sensitive control of finite state machines on an infinite horizon. II. SIAM J. Control Optim. 37 (1999), no. 4, 1048--1069 (electronic). w/Hernández-Hernández, Daniel

Deterministic nonlinear filtering. Dedicated to Ennio De Giorgi. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1997), no. 3-4, 435--454 (1998).

Stochastic analysis, control, optimization and applications. A volume in honor of W. H. Fleming. Edited by William M. McEneaney, G. George Yin and Qing Zhang. Systems & Control: Foundations & Applications. Birkhäuser Boston, Inc., Boston, MA, 1999. xxxiv+637 pp. ISBN: 0-8176-4078-9

Some results and problems in risk sensitive stochastic control. Mat. Apl. Comput. 16 (1997), no. 2, 99--115.

Risk-sensitive production planning of a stochastic manufacturing system. SIAM J. Control Optim. 36 (1998), no. 4, 1147--1170 (electronic). w/W. H.; Zhang, Q.

Asymptotics for the principal eigenvalue and eigenfunction of a nearly first-order operator with large potential. Ann. Probab. 25 (1997), no. 4, 1953--1994. w/Sheu, Shuenn-Jyi

Risk-sensitive control of finite state machines on an infinite horizon. I. SIAM J. Control Optim. 35 (1997), no. 5, 1790--1810. w/Hernández-Hernández, D.

Hedging in incomplete markets with HARA utility. J. Econom. Dynam. Control 21 (1997), no. 4-5, 753--782. w/Duffie, Darrell; Soner, H. Mete; Zariphopoulou, Thaleia

The risk-sensitive index and the $H\sb 2$ and $H\sb \infty$ norms for nonlinear systems. Math. Control Signals Systems 8 (1995), no. 3, 199--221. w/James, M. R.

Risk-sensitive control on an infinite time horizon. SIAM J. Control Optim. 33 (1995), no. 6, 1881--1915. w/McEneaney, William M.

Stochastic control and large deviations. Future tendencies in computer science, control and applied mathematics (Paris, 1992), 291--300, Lecture Notes in Comput. Sci., 653, Springer, Berlin, 1992.

Differential games for stochastic partial differential equations. Nagoya Math. J. 131 (1993), 75--107. w/Nisio, M.

Controlled Markov processes and viscosity solutions. Applications of Mathematics, 25. Springer-Verlag, New York, 1993. xvi+428 pp. ISBN: 0-387-97927-1 w/Soner, H. Mete

Risk sensitive optimal control and differential games. Stochastic theory and adaptive control (Lawrence, KS, 1991), 185--197, Lecture Notes in Control and Inform. Sci., 184, Springer, Berlin, 1992. McEneaney, William M.

A tribute to Wendell H. Fleming. SIAM J. Control Optim. 31 (1993), no. 2, 273--281. Berkovitz, L. D.; Shreve, Steven E.; Ziemer, William P.

Asymptotic series and exit time probabilities. Ann. Probab. 20 (1992), no. 3, 1369--1384. w/James, M. R.

Piecewise monotone filtering with small observation noise: numerical simulations. Applied stochastic analysis (New Brunswick, NJ, 1991), 108--120, Lecture Notes in Control and Inform. Sci., 177, Springer, Berlin, 1992. w/Zhang, Qing

Nonlinear filtering with small observation noise: piecewise monotone observations. Stochastic analysis, 153--168, Academic Press, Boston, MA, 1991. w/Zhang, Qing

Numerical methods for an optimal investment-consumption model. Math. Oper. Res. 16 (1991), no. 4, 823--841. w/Fitzpatrick, Ben G.

Piecewise monotone filtering in discrete-time with small observation noise. IEEE Trans. Automat. Control 36 (1991), no. 10, 1181--1186. w/Ji, D.; Salame, P.; Zhang, Q.

An optimal investment/consumption model with borrowing. Math. Oper. Res. 16 (1991), no. 4, 802--822. w/Zariphopoulou, Thaleia

Generalized solutions and convex duality in optimal control. Partial differential equations and the calculus of variations, Vol. I, 461--471, Progr. Nonlinear Differential Equations Appl., 1, Birkhäuser Boston, Boston, MA, 1989.

Edward James McShane (1904--1989). Notices Amer. Math. Soc. 36 (1989), no. 7, 828--830. w/Klee, Victor

Convex duality approach to the optimal control of diffusions. SIAM J. Control Optim. 27 (1989), no. 5, 1136--1155. w/Vermes, Domokos

A tribute to E. J. McShane. SIAM J. Control Optim. 27 (1989), no. 5, 909--915. w/Berkovitz, L. D.

Piecewise monotone filtering with small obervation noise. SIAM J. Control Optim. 27 (1989), no. 5, 1156--1181. w/Pardoux, É.

On the existence of value functions of two-player, zero-sum stochastic differential games. Indiana Univ. Math. J. 38 (1989), no. 2, 293--314. w/Souganidis, P. E.

Generalized solutions in the optimal control of diffusions. Stochastic differential systems, stochastic control theory and applications (Minneapolis, Minn., 1986), 119--127, IMA Vol. Math. Appl., 10, Springer, New York, 1988. w/Vermes, Domokos

Asymptotic expansions for Markov processes with Lévy generators. Appl. Math. Optim. 19 (1989), no. 2, 203--223. w/Soner, H. M.

A remark on the large deviations of an ergodic Markov process. Stochastics 22 (1987), no. 3-4, 187--199. w/Sheu, S.-J.; Soner, H. M.

Piecewise linear filtering with small observation noise. Analysis and optimization of systems (Antibes, 1988), 725--739, Lecture Notes in Control and Inform. Sci., 111, Springer, Berlin, 1988. w/Ji, D.; Pardoux, É.

Two-player, zero-sum stochastic differential games. Analyse mathématique et applications, 151--164, Gauthier-Villars, Montrouge, 1988. w/Souganidis, P. E.

Controlled Markov processes and viscosity solution of nonlinear evolution equations. Lezioni Fermiane. [Fermi Lectures] Scuola Normale Superiore, Pisa; Accademia Nazionale dei Lincei, Rome, 1986. 68 pp.

An optimal stochastic production planning problem with randomly fluctuating demand. SIAM J. Control Optim. 25 (1987), no. 6, 1494--1502. w/Sethi, S. P.; Soner, H. M.

Stochastic differential systems, stochastic control theory and applications. Proceedings of the workshop held at the University of Minnesota, Minneapolis, Minnesota, June 9--19, 1986. Edited by Wendell Fleming and Pierre-Louis Lions. The IMA Volumes in Mathematics and its Applications, 10. Springer-Verlag, New York, 1988. xiv+609 pp. ISBN: 0-387-96641-2

Steele prizes awarded at the summer meeting in Salt Lake City. Notices Amer. Math. Soc. 34 (1987), no. 6, 875--878.

PDE-viscosity solution approach to some problems of large deviations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 13 (1986), no. 2, 171--192. w/Souganidis, Panagiotis E.

Stochastic variational formula for fundamental solutions of parabolic PDE. Appl. Math. Optim. 13 (1985), no. 3, 193--204. w/Sheu, Sheunn Jyi

A PDE approach to some large deviations problems. Nonlinear systems of partial differential equations in applied mathematics, Part 1 (Santa Fe, N.M., 1984), 441--447, Lectures in Appl. Math., 23, Amer. Math. Soc., Providence, RI, 1986. Souganidis, P. E.

Erratum: "Asymptotic series and the method of vanishing viscosity". Indiana Univ. Math. J. 35 (1986), no. 4, 925. w/Souganidis, P. E.

Asymptotic series and the method of vanishing viscosity. Indiana Univ. Math. J. 35 (1986), no. 2, 425--447. w/Souganidis, P. E.

Optimal control of Markov processes. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983), 71--84, PWN, Warsaw, 1984.

A stochastic control approach to some large deviations problems. Recent mathematical methods in dynamic programming (Rome, 1984), 52--66, Lecture Notes in Math., 1119, Springer, Berlin, 1985.

Advances in filtering and optimal stochastic control. Proceedings of the IFIP-WG 7/1 working conference held in Cocoyoc, February 1--6, 1982. Edited by W. H. Fleming and L. G. Gorostiza. Lecture Notes in Control and Information Sciences, 42. Springer-Verlag, Berlin, 1982. viii+392 pp. ISBN: 3-540-11936-1

Logarithmic transformations and stochastic control. Advances in filtering and optimal stochastic control (Cocoyoc, 1982), 131--141, Lecture Notes in Control and Inform. Sci., 42, Springer, Berlin, 1982.

Recent mathematical methods in dynamic programming. Proceedings of the conference held in Rome, March 26--28, 1984. Edited by I. Capuzzo Dolcetta, W. H. Fleming and T. Zolezzi. Lecture Notes in Mathematics, 1119. Springer-Verlag, Berlin, 1985. iii+202 pp. ISBN: 3-540-15217-2

On stochastic relaxed control for partially observed diffusions. Nagoya Math. J. 93 (1984), 71--108. w/Nisio, M.

Stochastic calculus of variations and mechanics. J. Optim. Theory Appl. 41 (1983), no. 1, 55--74.

Optimal control and nonlinear filtering for nondegenerate diffusion processes. Stochastics 8 (1982/83), no. 1, 63--77. w/Mitter, Sanjoy K.

Optimal control for partially observed diffusions. SIAM J. Control Optim. 20 (1982), no. 2, 261--285. w/Pardoux, Étienne

Nonlinear semigroup for controlled partially observed diffusions. SIAM J. Control Optim. 20 (1982), no. 2, 286--301.

Optimal exit probabilities and differential games. Appl. Math. Optim. 7 (1981), no. 3, 253--282. w/Tsai, Chun Ping

Stochastic control under partial observations. Analysis and optimization of systems (Proc. Fourth Internat. Conf., Versailles, 1980), pp. 308--317, Lecture Notes in Control and Information Sci., 28, Springer, Berlin-New York, 1980.

Exit probabilities for diffusions depending on small parameters. Analysis and optimisation of stochastic systems (Proc. Internat. Conf., Univ. Oxford, Oxford, 1978), pp. 141--145, Academic Press, London-New York, 1980.

Measure-valued processes in the control of partially-observable stochastic systems. Appl. Math. Optim. 6 (1980), no. 3, 271--285.

Some measure-valued Markov processes in population genetics theory. Indiana Univ. Math. J. 28 (1979), no. 5, 817--843. w/Viot, Michel

Exit probabilities and optimal stochastic control. Appl. Math. Optim. 4 (1977/78), no. 4, 329--346.

Inclusion probability and optimal stochastic control. Analyse et contrôle de systèmes (Papers, IRIA Sem., Rocquencourt, 1977), pp. 53--61, IRIA, Rocquencourt, 1977.

Minimum exit probabilities and differential games. Differential games and control theory (Proc. Third Kingston Conf., Part A, Univ. Rhode Island, Kingston, R.I., 1978), pp. 67--75, Lecture Notes in Pure and Appl. Math., 44, Dekker, New York, 1979. Tsai, Chun Ping

Equilibrium distributions of continuous polygenic traits. SIAM J. Appl. Math. 36 (1979), no. 1, 148--168.

Some measure-valued population processes. Stochastic analysis (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1978), pp. 97--108, Academic Press, New York-London, 1978. Viot, M.

{\cyr Optimal\cprime noe upravlenie determinirovannymi i stokhasticheskimi sistemami}. (Russian) [Deterministic and stochastic optimal control] Translated from the English by M. G. Butrim and P. K. Katy\v sev. Edited by A. N. \v Sirjaev. "Mir", Moscow; distributed by Imported Publications, Chicago, Ill., 1978. 316 pp. Ri\v sel, R.

Generalized solutions in optimal stochastic control. Differential games and control mtheory, II (Proc. 2nd Conf., Univ. Rhode Island, Kingston, R.I., 1976), pp. 147--165. Lecture Notes in Pure and Appl. Math., 30. Dekker, New York, 1977.

Optimal inclusion probability and differential games. Analyse et contrôle de systèmes (Papers, IRIA Sem., Rocquencourt, 1977), pp. 63--68. IRIA, Rocquencourt, 1977. Tsai, Chun Ping

Some stochastic systems depending on small parameters. Dynamical systems (Proc. Internat. Sympos., Brown Univ., Providence, R.I., 1974), Vol. I, pp. 103--114. Academic Press, New York,1976. Tsai, C. P.

Deterministic and stochastic optimal control. Applications of Mathematics, No. 1. Springer-Verlag, Berlin-New York, 1975. vii+222 pp. w/Rishel, Raymond W.

Optimal stochastic control. Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 3, pp. 163--167. Gauthier-Villars, Paris, 1971.

Functions of several variables. Second edition. Undergraduate Texts in Mathematics. Springer-Verlag, New York-Heidelberg, 1977. xi+411 pp.

Dynamical systems with small stochastic terms. Techniques of optimization (Fourth IFIP Colloq. Optimization Techniques, Los Angeles, Calif., 1971), pp. 325--333. Academic Press, New York, 1972.

A selection-migration model in population genetics. J. Math. Biol. 2 (1975), no. 3, 219--233.

Control theory and the calculus of variations. Based on the lectures presented at the Workshop on Calculus of Variations and Control Theory, University of California, Los Angeles, July 1968. Edited by A. V. Balakrishnan. Dedicated to Magnus R. Hestenes. Academic Press, New York-London, 1969. xiii+422 pp.

Distributed parameter stochastic systems in population biology. Control theory, numerical methods and computer systems modelling (Internat. Sympos., IRIA LABORIA, Rocquencourt, 1974), pp. 179--191. Lecture Notes in Econom. and Math. Systems, Vol. 107, Springer, Berlin, 1975.

International Conference on Differential Equations. Proceedings of an International Conference on Differential Equations held at the University of Southern California, Los Angeles, Calif., September 3--7, 1974. Edited by H. A. Antosiewicz. Academic Press, Inc. [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. xix+834 pp.

{\cyr Mekhanika: Periodicheski\u\i sbornik perevodov inostrannykh state\u\i } {1974}, {\cyr vyp.} 2(144). (Russian) [Mechanics: Periodical collection of translations of foreign articles 1974, no. 2(144)] Izdat. Mir'', Moscow, 1974. 143 pp.

Stochastically perturbed dynamical systems. Papers arising from a Conference on Stochastic Differential Equations (Univ. Alberta, 1972). Rocky Mountain J. Math. 4 (1974), 407--433.

Optimal control of diffusion processes. Stochastic differential equations (Proc. SIAM-AMS Sympos. Appl. Math., New York, 1972), pp. 163--171. SIAM-AMS Proc., Vol. VI, Amer. Math. Soc., Providence, R.I., 1973.

{\cyr Tselochislennye potoki i minimal\cprime nye poverkhnosti}. (Russian) [Integral currents and minimal surfaces] A collection of articles translated from the English and Italian by Ju. S. Il\cprime ja\v senko. Izdat. Mir'', Moscow, 1973. 203 pp.

Stochastic control for small noise intensities. SIAM J. Control 9 (1971), 473--517.

Nonlinear partial differential equations---Probabilistic and game theoretic methods. 1971 Problems in Non-Linear Analysis (C.I.M.E., IV Ciclo, Varenna, 1970) pp. 95--128 Edizioni Cremonese, Rome

Optimal continuous-parameter stochastic control. SIAM Rev. 11 1969 470--509.

Lectures on the calculus of variations and optimal control theory. Foreword by Wendell H. Fleming W. B. Saunders Co., Philadelphia-London-Toronto, Ont. 1969 xi+331 pp.Young, L. C.

Stochastic Lagrange multipliers. 1967 Mathematical Theory of Control (Proc. Conf., Los Angeles, Calif., 1967) pp. 433--440 Academic Press, New York

Correlation theory of statistically optimal systems. Translated from the Russian by Scripta Technica, Inc. Edited by Wendell H. Fleming W. B. Saunders Co., Philadelphia, Pa.-London-Toronto, Ont. 1969 x+370 pp. Andreyev, N. I.

Optimal control of partially observable diffusions. SIAM J. Control 6 1968 194--214.

The Cauchy problem for a nonlinear first order partial differential equation. J. Differential Equations 5 1969 515--530.

Optimal control of diffusion processes. 1966 Functional Analysis and Optimization pp. 67--84 Academic Press, New York

Duality and a priori estimates in Markovian optimization problems. J. Math. Anal. Appl. 16 1966 254--279.

On the existence of optimal stochastic controls. J. Math. Mech. 15 1966 777--794. w/Nisio, Makiko

Flat chains over a finite coefficient group. Trans. Amer. Math. Soc. 121 1966 160--186.

The Cauchy problem for degenerate parabolic equations. J. Math. Mech. 13 1964 987--1008.

Functions of several variables. Addison-Wesley Publishing Co., Inc., Reading, Mass.-London 1965 x+337 pp.

The convergence problem for differential games. II. 1964 Advances in game theory pp. 195--210 Princeton Univ. Press, Princeton, N.J.

Some extremal questions for simplicial complexes. IV. The algebraic and the geometric resultant, and application of variational methods. Rend. Circ. Mat. Palermo (2) 12 1963 200--210. w/Young, L. C.

Some questions in the theory of moments. translated by W. Fleming and D. Prill. Translations of Mathematical Monographs, Vol. 2 American Mathematical Society, Providence, R.I. 1962 v+265 pp. Aheizer, N. I.; Krein, M.

On the oriented Plateau problem. Rend. Circ. Mat. Palermo (2) 11 1962 69--90.

Some Markovian optimization problems. J. Math. Mech. 12 1963 131--140.

The convergence problem for differential games. J. Math. Anal. Appl. 3 1961 102--116.

Functions whose partial derivatives are measures. Illinois J. Math. 4 1960 452--478.

Normal and integral currents. Ann. of Math. (2) 72 1960 458--520. w/Federer, Herbert

Irreducible generalized surfaces. Riv. Mat. Univ. Parma 8 1957 251--281.

An integral formula for total gradient variation. Arch. Math. 11 1960 218--222. w/Rishel, Raymond

Nondegenerate surfaces of finite topological type. Trans. Amer. Math. Soc. 90 1959 323--335.

Nondegenerate surfaces and fine-cyclic surfaces. Duke Math. J. 26 1959 137--146.

Functions whose partial deriatives are measures. Bull. Amer. Math. Soc. 64 1958 364--366.

Functions with generalized gradient and generalized surfaces. Ann. Mat. Pura Appl. (4) 44 1957 92, 93--103.

A note on differential games of prescribed duration. 1957 Contributions to the theory of games, vol. 3 pp. 407--412 Annals of Mathematics Studies, no. 39 Princeton University Press, Princeton, N.J.

On differential games with integral payoff. Contributions to the theory of games, vol. 3, pp. 413--435. Annals of Mathematics Studies, no. 39. Princeton University Press, Princeton, N. J., 1957. w/Berkovitz, L. D.

Generalized surfaces with prescribed elementary boundary. Rend. Circ. Mat. Palermo (2) 5 (1956), 320--340 (1957). w/Young, L. C.

Representations of generalized surfaces as mixtures. Rend. Circ. Mat. Palermo (2) 5 (1956), 117--144. w/Young, L. C.

An example in the problem of least area. Proc. Amer. Math. Soc. 7 (1956), 1063--1074.

Variational problems with constraints. Ann. Mat. Pura Appl. (4) 41 (1956), 301--323. w/Bellman, R.;Widder, D. V.

On a class of games over function space and related variational problems. Ann. of Math. (2) 60, (1954). 578--594.

A generalized notion of boundary. Trans. Amer. Math. Soc. 76, (1954). 457--484. w/Young, L. C.

Logarithmic transformations with applications in probability and stochastic control. Modeling and control of systems in engineering, quantum mechanics, economics and biosciences (Sophia-Antipolis, 1988), 309--311, Lecture Notes in Control and Inform. Sci., 121, Springer, Berlin, 1989.

A PDE approach to asymptotic estimates for optimal exit probabilities. Stochastic differential systems (Marseille-Luminy, 1984), 281--285, Lecture Notes in Control and Inform. Sci., 69, Springer, Berlin, 1985. w/Souganidis, Panagiotis E.