Mark H.A. Davis: 20th Century Publications

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Books

  1. Linear Estimation and Stochastic Control, Chapman and Hall, London/Halsted Press, New York 1977 [MR57,15678]
  2. Lineinoe Otsenivanie i Stochasticheskoe Upravlenie, Nauka, Moscow 1984 {Russian translation of Linear Estimation and Stochastic Control, with revisions} [MR83h:93048]
  3. Lectures on Stochastic Control and Nonlinear Filtering, Narosa, New Delhi/ Springer-Verlag, Berlin 1985 [MR86c:93118]
  4. Stochastic Modelling and Control, Monographs on Statistics and Applied Probability 24, Chapman and Hall, London/New York 1985 [MR87f:93001](with R.B. Vinter)
  5. Markov Models and Optimization, Monographs on Statistics and Applied Probability 49, Chapman and Hall, London/New York, 1993
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Refereed Journal Articles

  1. Dynamic programming conditions for partially-observed stochastic systems, SIAM J Control 11(1973) 226-261 (with P P Varaiya) [MR 48,8184]
  2. On the existence of optimal policies in stochastic control, SIAM J Control 11(1973)587-594 [MR48,3579]
  3. Information states for linear stochastic systems, J Math Anal Appl(1972) 384-402 (with P P Varaiya)
  4. On the multiplicity of an increasing family of sigma-fields, Ann Prob 2 (1974) 958-963 (with P Varaiya) [MR51,6980]
  5. Nonlinear filtering with counting observations, IEEE Trans Information Theory IT-21 (1975) 143-149 (with A Segall and T Kailath)
  6. The application of nonlinear filtering to fault detection in linear systems, IEEE Trans Automatic Control AC-20 (1975) 257-259
  7. On stochastic differentiation,Theory of Probability and its Applications. (USSR) 20 (1975) 887-892 [MR 52,15672]
  8. The separation priciple in stochastic control via Girsanov solutions, SIAM J Control and Optimization 14 (1976) 176-188
  9. The representation of martingales of jump processes, SIAM J Control and Optimization 14 (1976) 623-638 [MR54,6262]
  10. Martingales of Wiener and Poisson processes, J London Math Soc (2) 13 (1976)
  11. Exact and approximate filtering in signal detection: an example, IEEE Trans Information Theory IT-23 (1977) 768-772 (with E Andreadakis)
  12. Optimal control of a jump process, Z Wahrscheinlichkeitstheorie ver Geb 40 (1977) 183-202 (with R J Elliott) [MR58,7824]
  13. The general point process disorder problem, IEEE Trans Information Theory IT-23 (1977) 538-540 (with C B Wan) [MR57,15699]
  14. A direct proof of innovations/observations equivalence for gaussian processes, IEEE Trans Information Theory IT-24 (1978) 252-254 [MR 80j:60057]
  15. Existence of optimal controls for stochastic jump processes, SIAM J Control and Optimization 17 (1979) 511-524 (with C B Wan) [MR 80j:93145]
  16. "Predicted miss" problems in stochastic optimal control, Stochastics 2 (1979) 197-209 (with J M C Clark) [MR80i:93065]
  17. Stochastic control by measure transformation: a general existence result, Information Science 21 (1980), 195-208 (with M Kohlmann)
  18. Functionals of diffusion processes as stochastic integrals, Math Proc Cambridge Phil Soc 87 (1980) 157-166 [MR80j:60038][PDF]
  19. Capacity and cutoff rate for Poisson-type channels, IEEE Trans Information Theory IT-26 (1980) 710-715 [MR81k:94023]
  20. On a multiplicative functional arising in nonlinear filtering theory,Z Wahrscheinlichkeitstheorie ver. Geb. 54 (1980) 125-139 [MR82i:60074]
  21. Optimal play in a stochastic differential game, SIAM J Control and Optimization 19 (1981) 543-554 (with R.J. Elliott) [MR82f:93069]
  22. Factorization of a multiplicative functional of nonlinear filtering theory, Systems and Control Letters 1 (1981) 49-53 [MR84i:93136]
  23. New approach to filtering for nonlinear systems, Proc IEE (D)128 (1981) 166-172 [MR 83c:93051]
  24. A note on a comparison theorem for equations with different diffusions, Stochastics 6 (1982) 147-149 (with L I Galchuk) [MR83k:60057]
  25. A pathwise solution of the equations of nonlinear filtering, Theory of Probability and its Appl (USSR) 27 (1982) 160-167 [MR83d:60049]
  26. On a problem of D R Cox, Ann New York Acad Sci 410 (1983) 129-132 [MR86m:62170]
  27. Piecewise-deterministic Markov processes: a general class of non-diffusion stochastic models (with discussion), J Royal Statist Soc (B) 46 (1984) 353-388 [MR87g:60062]
  28. Optimal timing of capacity expansion, J Economic Dynamics and Control 10 (1986) 89-92 (with Z Carvalhais)
  29. Pathwise nonlinear filtering for non-degenerate diffusions with noise correlation, SIAM J Control and Optimization 25(1987) 260-278(with M P Spathopoulos) [MR88f:93112]
  30. Optimal capacity expansion under uncertainty, Advances in Applied Probability 19 (1987) 156-176 (with M A H Dempster, S P Sethi and D Vermes)[MR88a:90103]
  31. The martingale maximum principle and the allocation of labour surplus, J Economic Dynamics and Control 11 (1987) 210-217 (with G Gomez) [MR89d:90063]
  32. Approximations for optimal stopping of a piecewise-deterministic process, Math of Control, Signals and Systems 1 (1988) 123-146 (with O L V Costa) [MR89h:90249]
  33. Wiener space derivatives for functionals of diffusions on manifolds, Nonlinearity 1(1988) 241-251 [MR89i:60116]
  34. Anticipative LQG control, IMA J Mathematical Control and Information 6 (1989) 259-265 [MR91c:49057]
  35. Impulse control of piecewise-deterministic processes, Mathematics of Control, Signals and Systems 2 (1989) 187-206 (with O L V Costa) [MR90i:93146]
  36. On the minimum priciple principle for controlled diffusions on manifolds, SIAM J Control and Optimization 27(1989)1092-1107 (with M.P.Spathopoulos) [MR91b:49025]
  37. Strong consistency of the PLS criterion for order determination of autoregressive models, Annals of Statistics 17 (1989) 941-946 (with E M Hemerly) [MR91e:62235]
  38. Recursive order estimation of stochastic control systems, Mathematical Systems Theory 22 (1989),323-346 (with E M Hemerly) [MR91c:93070]
  39. Portfolio selection with transaction costs, Math. of Operations Research 15 (1990) 676-713 (with A.R.Norman) [MR92b:90036] [PDF]
  40. Recursive order estimation of autoregressions without bounding the model set, J Royal Statist. Soc.(B) 53 (1991), 201-210 (with E M Hemerly) [MR92d:62122]
  41. A deterministic approach to stochastic optimal control with application to anticipative control, Stochastics and Stochastics Reports 40 (1992) 203-256 (with G Burstein) [PDF]
  42. Reducibility and unobservability of Markov processes, IEEE Trans Automatic Control AC-37, (1992) 505-508 (with V Lasdas)
  43. European option pricing with transaction costs, SIAM J. Control and Optimization 31 (1993) 470-493 (with V G Panas and T Zariphopoulou)
  44. A problem of singular control with discretionary stopping, Ann. Appl. Prob. 4 (1994) 226-240 (with M. Zervos)
  45. A note on super-replicating strategies, Phil. Trans. R. Soc. Lond. A (1994) 347, 485-494 (with J.M.C. Clark)
  46. The writing price of a European contingent claim under proportional transaction costs, Computational and Applied Math. 13 (1994) 115-157 (with V.G. Panas)
  47. A new proof of the discrete-time LQG optimal control theorems, IEEE Trans Automatic Control AC-49 (1995) 1450-1453
  48. Permanent health insurance: a case study in piecewise-deterministic Markov modelling, Mitteilungen der Schweiz. Vereinigung der Versicherungsmathematiker, Heft 2 (1995) 177-212 (with M.H. Vellekoop)
  49. A target recognition problem: sequential analysis and optimal control, SIAM J. Control and Optimization 34 (1996) 2116-2132 (with M. Farid)
  50. A Markovian analysis of the M/D/1 Queue with finite buffer, Proceedings of the Royal Society (A) 453 (1997) 1947-1962 (with J.M. Howl)
  51. A new order estimation technique for time series modelling, IEEE Trans Automatic Control 42 (1997) 402-403 (with W.X. Zheng)
  52. A note on the forward measure, Finance and Stochastics 2 (1998) 19-28
  53. A pair of explicitly solvable singular stochastic control problems, Applied Math. and Optimization 38 (1998) 327-352 (with M. Zervos)
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Other publications

  1. Optimal control of a degenerate markovian system, in Recent Mathematical Developments in Control, ed. D J Bell, New York/London 1973
  2. Linear and nonlinear filtering with counting observations, 8th Princeton Conference on Information Science and Systems (with A Segall and T Kailath) 1974
  3. Estimation of point processes, Proc IFAC Symposium on Stochastic Control, Budapest 1974 (with A Segall and T Kailath)
  4. On the separation principle, Proc 5th Symposium on Nonlinear Estimation and Applications, San Diego, California 1974
  5. A note on the Poisson disorder problem, in Mathematical Control Theory, Banach Center Publications vol 1, PWN, Warszawa 1976
  6. The structure of jump processes and related control problems, Math Programming Study 6 (1976) 2-14 [MR57,15685]
  7. The martingale approach in stochastic control, Report TRITA-MAT-1977-11, Royal Institute of Technology, Stockholm, Sweden, 1977
  8. Detection, mutual information and feedback encoding: applications of stochastic calculus, in Communications Systems and Random Process Theory, ed J K Skwirzinski, Sijthoff & Noordhoff, Alphen aan den Rijn, 1978 [PDF]
  9. Martingale integrals and stochastic calculus, in Communication Systems and Random Process Theory, ed J K Skwirzinski, NATO Advanced Study Institute Series E No 45, Sijthoff & Noordhoff, Alphen aan den Rijn, 1978
  10. Nonlinear semigroups in the control of partially observed stochastic systems,in Measure Theory and Applications to Stochastic Analysis, Lecture Notes in Mathematics 695, Springer-Verlag Berlin 1978 [MR80e:93137]
  11. Martingale methods in stochastic control, in Stochastic Control and Stochastic Differential Systems, Lecture Notes in Control and Information Sciences 16 Springer-Verlag, Berlin 1979 [MR 82b:93051]
  12. Pathwise solutions and multiplicative functionals in nonlinear filtering, Proc 18th IEEE Conference on Decision and Control, Fort Lauderdale, Florida 1979
  13. Review of Stochastic Optimal Control: the Discrete-Time Case by D Bertsekas and S E Shreve, IEEE Trans Automatic Control AC-25 (1980) 1254-1255
  14. The principle of optimality for controlled jump processes, in Analysis and Optimization of Stochastic Systems, ed O L R Jacobs et al., Academic Press, London/New York 1980
  15. Comments on Weaker conditions for innovations informational equivalence in the independent gaussian case IEEE Trans Automatic Control AC-25 (1980) 607-608
  16. Computational problems in nonlinear filtering, in Analysis and Optimization of Systems, Lecture Notes in Control and Information Sciences 28, Springer-Verlag, Berlin 1980 (with P H Wellings)[MR 83d:93060]
  17. Review of Stochastic Models, Estimation and Control by P S Maybeck, Proc IEE (D) 128 (1981)
  18. Pathwise nonlinear filtering, in Stochastic Systems: the Mathematics of Filtering and Identification, ed. M Hazewinkel & J C Willems, D Reidel,Dordrecht 1981
  19. An introduction to nonlinear filtering, in Stochastic Systems: the Mathematics of Filtering and Identification, ed M Hazewinkel and J C Willems, D Reidel, Dordrecht, 1981 (with S. I. Marcus)[PDF]
  20. Stochastic control with tracking of exogenous parameters,in Stochastic Differential Systems,Lecture Notes in Control & Information Sciences 43, Springer-Verlag, Berlin 1982 [MR86m:93099]
  21. Stochastic control with noisy observations, in Advances in Filtering and Optimal Control, Lecture Notes in Control and Information Sciences 42, Springer-Verlag, Berlin 1982 [MR86h:93061]
  22. The martingale theory of point processes and its application to the analysis of failure time data, in Electronic Systems Effectiveness and Life-Cycle Costing, ed J K Skwirzinski, NATO ASI Series F, Springer-Verlag, Berlin 1983
  23. On the stochastic maximum principle for manifold-valued processes,Proc 24th IEEE Conference on Decision and Control,Ft Lauderdale,Florida, 1337-1342, 1985 (with M P Spathopoulos and T Yoneyama)
  24. Point process models: some current techniques, in Biorythms and Epilepsy, ed A Martins de Silva, C D Binnie & H Meinardi,Raven Press, New York 1985
  25. Review of Recursive Estimation and Control for Stochastic Systems by Han-Fu Chen, Proc IEE (D) 1986
  26. Nonlinear filtering and stochastic flows, Proc International Congress of Mathematicians, Berkeley, California, 1986 [MR98h:60067]
  27. Pathwise nonlinear filtering with observations on a manifold, Proc 25th IEEE Conference on Decision and Control, Athens, 1028-1029, 1986 (with M P Spathopoulos)
  28. Control of piecewise-deterministic processes via discrete-time dynamic programming, in Stochastic Differential Systems, Lecture Notes in Control and Information Sciences 78, 140-150, Springer-Verlag, Berlin 1986 [MR88g:49027]
  29. Optimal stochastic control: general aspects, in Encyclopaedia of Systems and Control, ed M G Singh, Pergamon Press Oxford,1987
  30. The semimartingale approach to the optimal resource allocation in the controlled labour-surplus economy in Stochastic Processes: Mathematics and Physics II, Lecture Notes in Mathematics 1250, pp 36-74, Springer-Verlag, Berlin 1987 (with G Gomez) [MR89d:90062]
  31. Optimal Control of diffusions on manifolds, in Analysis and Control of Nonlinear Systems, ed. C I Byrne s, C F Martin & R E Saeks, North Holland, Amsterdam, 1988
  32. Local time on the stock exchange, in Stochastic Calculus in Application, ed. J R Norris, Pitman Research Notes in Mathematics 197, Longman, London 1988 [MR90h:90018]
  33. Optimal Control of piecewise-deterministic processes, in Differential Equations and Applications (Proc 3rd Conference on Differential Equations, Ruse, Bulgaria 1985), Publ Angel Kancec Tech Univ Ruse, 1988 [MR88m:49021]
  34. Order determination and adaptive control of ARX models using the PLS criterion, in Stochastic Differential Systems, ed.N Christopeit, Lecture Notes in Control and Information Sciences 126, Springer-Verlag, Berlin 1989 (with E M Hemerly)
  35. A review of the statistical theory of signal detection, in Gravitational Wave Data Analysis,ed B F Schutz, NATO ASI Series, Kluwer, Dordrecht, 1989
  36. A piecewise deterministic process approach to target motion analysis, Proc. 28th IEEE Conference on Decision and Control, Tampa, Florida, December 1395-1396,1989 (with V. Lasdas)
  37. An image analysis method for closing the roll loop, Proc. 28th IEEE Conference on Decision and Control, Tampa, Florida, 2371-2372,1989 (with M S Zucker)
  38. On the approximate stochastic realization problem, Proc. 30th IEEE Conference on Decision and Control, Brighton, 1991, pp 1698-1699 (with P Fotopoulos)
  39. European option pricing with transaction costs, Proc. 30th IEEE Conference on Decision and Control, Brighton, 1991, pp 1299-1304 (with V G Panas)
  40. Clustering algorithms for Bayesian fault detection, Proc. 30th IEEE Conference on Decision and Control, Brighton, 1991, pp 674-675 (with S. Lasdas and D.J. Salmond)
  41. On the value of information in controlled diffusion processes, in Stochastic Analysis: Liber Amicorum for Moshe Zakai, eds E Mayer-Wolf, A Shwartz and O. Zeitouni 1991, pp 125-138 (with M A H Dempster and R J Elliott)
  42. Jump processes and their martingales, Preprint 91-10, Mathematics Institute, University of Oslo, 1991
  43. Anticipative stochastic control, Proc. 30th IEEE Conference on Decision and Control, Brighton, 1991, pp 1830-1835 (with G Burstein)
  44. Two quick proofs of the Black-Scholes option pricing formula, Preprint 91-13, Mathematics Institute, University of Oslo, 1991
  45. Applied Stochastic Analysis, Stochastics Monographs 5, Gordon & Breach, London, 1991 [MR91m:93003] (with R.J. Elliott)
  46. Anticipative LQG Control II, in Applied Stochastic Analysis, eds.M H A Davis and R J Elliott, Gordon and Breach, London 1991 [MR92d:93123]
  47. Dynamic optimization: a grand unification, Proc. 31st IEEE Conference on Decision and Control, Tucson, 1992
  48. A stochastic realization approach to order determination in time series modelling, Proc. 31st IEEE Conference on Decision and Control, Tucson, 1992 (with Wei-Xing Zheng)
  49. Stochastic partially observed optimal control via deterministic infinite-dimensional control: on the value of information in partially-observed diffusions, Proc. 31st IEEE Conference on Decision and Control, Tucson, 1992 (with G Burstein)
  50. On the relation between deterministic and stochastic optimal control, in Stochastic Partial Differential Equations and Applications, eds G. Da Prato and L. Tubaro, Pitman Research Notes in Mathematics 268, Longman, London 1992, pp 124-157 (with G Burstein)
  51. Random conservation laws and global solutions of nonlinear SPDE; application to the HJB-SPDE of anticipative control, in Stochastic Partial Differential Equations and their Applications, eds B.L.Rozovskii and R. Sowers, Lecture Notes in Control and Information Sciences 176, Springer-Verlag, Berlin, 1992, pp 43-53 (with G
  52. Stratonovich Integral, article in the Soviet Encyclopaedia of Mathematics, English translation ed. M. Hazewinkel, Kluwer, Dordrecht, 1993
  53. A deterministic approach to optimal stopping, in Probability, Statistics and Optimization: a Tribute to Peter Whittle, ed F.P. Kelly, Wiley, Chichester 1994, (with I. Karatzas)[PDF]
  54. Review of "Controlled Markov Processes and Viscosity Solutions" by W.H.Fleming and H.M.Soner, Bull. AMS 31 (1994) 75-85
  55. Mathematical Finance, eds M.H.A.Davis, D. Duffie, S.E.Shreve, IMA Volumes in Mathematics and its Applications 65, Springer-Verlag, New York 1995 New York 1995 (with D. Duffie, W.H. Fleming and S.E.Shreve)
  56. American options and transaction fees, in Mathematical Finance, eds. M.H.A. Davis et al., Springer-Verlag, New York 1995 (with T. Zariphopoulou) [PDF]
  57. European option pricing via a utility maximization method, in Quantitative Methods, Supercomputers and AI in Finance, ed S. Zenios, Stanley Thornes, Cheltenham, 1995 (with V G Panas)
  58. Interest rate models and instruments, Introduction to Mitsubishi Finance Risk Directory 1996, Risk Publications, London 1995 (with J G B Beumee and H Lee)
  59. Optimal consumption and exploration: a case study in piecewise-deterministic Markov modelling, Annals of Operations Research, 1997 (with M. Farid)
  60. Pricing and hedging methodologies for credit derivatives, Global Derivatives 98, ICBI Conferences, Paris 1998
  61. Option pricing in incomplete markets, in Mathematics of Derivative Securities, eds M.A.H. Dempster and S.R. Pliska, Cambridge University Press 1998 [PDF]
  62. Option valuation and hedging with basis risk, in "Advances in System Theory", ed. T. Djaferis, Kluwer Academic Publishers, 1999
  63. Piecewise-deterministic processes and viscosity solutions, in Stochastic Analysis, Control, Optimization and Applications, eds W. M.McEneaney, G.G. Yin and Q. Zhang, Birkhauser, Boston 1999 (with M. Farid)
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