Pitman Research Notes in Mathematics Series Main Editors H. Brezls, Universite de Paris R. G. Douglas, State University of New York at Stony Brook A. Jeffrey, University of Newcastle-upon-Tyne (Founding Editor) Editorial Board R. Aris, University of Minnesota B. Lawson, State University of New York at A. Bensoussan, INRIA, France Stony Brook W. Burger, Universitlit Karlsruhe W. F. Lucas, Cornell University J. Douglas Jr, University of Chicago R. E. Meyer, University of Wisconsin-Madison R. J. Elliott, University of Hull J. Nitsche, Universitlit Frei burg G. Fichera, Universita di Roma L. E. Payne, Cornell University R. P. Gilbert, University of Delaware G. F. Roach, University of Strathclyde R. Glowinski, Universite de Paris J. H. Seinfeld, California Institute of K. P. Hadeler, Universitlit Tiibingen Technology K. Kirchglissner, Universitlit Stuttgart I. N. Stewart, University of WarwiCJ S. J. Taylor, University of Virginia Submission of proposals for consideration Suggestions for publication, in the form of outlines and representative samples, are invited by the Editorial Board for assessment. Intending authors should approach one of the main editors or another member of the Editorial Board, citing the relevant AMS subject classifications. Alternatively, outlines may be sent directly to the publisher's offices. Refereeing is by members of the board and other mathematical authorities in the topic concerned, throughout the world. · Preparation of accepted manuscripts On acceptance of a proposal, the publisher will supply full instructions for the preparation of manuscripts in a form suitable for direct photo-lithographic reproduction. Specially printed grid sheets are provided and a contribution is offered by the publisher towards the cost of typing. Word processor output, subject to the publisher's approval, is also acceptable. Illustrations should be prepared by the authors, ready for direct reproduction without further improvement. The use of hand-drawn symbols should be avoided wherever possible, in order to maintain maximum clarity of the text. The publisher will be pleased to give any guidance necessary during the preparation of a typescript, and will be happy to answer any queries. Important note In order to avoid later retyping, intending authors are strongly urged not to begin final preparation of a typescript before receiving the publisher's guidelines and special paper. In this way it is hoped to preserve the uniform appearance of the series. Longman Scientific & Technical Longman House Burnt Mill Harlow, Essex, UK (tel (0279) 26721) Titles in this series Improperly posed boundary value problems 28 Constructive functional analysis A Carasso and A P Stone DS Bridges 2 Lie algebras generated by finite dimensional 29 Elongational flows: Aspects of the behaviour ideals of model elasticoviscous fluids IN Stewart CJ SPetrie 3 Bifurcation problems in nonlinear 30 Nonlinear analysis and mechanics: elasticity Heriot-Watt Symposium Volume III RWDickey RJKnops 4 Partial differential equations in the complex 31 Fractional calculus and integral transforms of domain generalized functions DLColton AC McBride 5 Quasilinear hyperbolic systems and waves 32 Complex manifold techniques in theoretical A Jeffrey physics 6 Solution of boundary value problems by the D E Lerner and P D Sommers method of integral operators 33 Hilbert's third problem: scissors congruence DLColton C-HSah 7 Taylor expansions and catastrophes 34 Graph theory and combinatorics T Poston and I N Stewart RJWilson 8 Function theoretic methods in differential 35 The Tricomi equation with applications to the equations theory of plane transonic flow RP Gilbert and R J Weinacht ARManwell 9 Differential topology with a view to 36 Abstract differential equations applications SDZaidman D R J Chillingworth 37 Advances in twistor theory IO Characteristic classes of foliations LP Hughston and RS Ward H VPittie 38 Operator theory and functional analysis 11 Stochastic integration and generalized I Erdelyi martingales 39 Nonlinear analysis and mechanics: A UKussmaul Heriot-Watt Symposium Volume IV 12 Zeta-functions: An introduction to algebraic RJ Knops geometry 40 Singular systems of differential equations AD Thomas S LCampbell 13 Explicit a priori inequalities with applications to 41 N-dimensional crystallography boundary value problems R L E Schwarzenberger V G Sigillito 42 Nonlinear partial differential equations in 14 Nonlinear diffusion physical problems W E Fitzgibbon III and HF Walker DGram 15 Unsolved problems concerning lattice points 43 Shifts and periodicity for right invertible JHammer operators 16 Edge-colourings of graphs D Przeworska-Rolewicz S Fiorini and R J Wilson 44 Rings with chain conditions 17 Nonlinear analysis and mechanics: A W Chatters and C R Hajarnavis Heriot-Watt Symposium Volume I 45 Moduli, deformations and classifications of RJKnops compact complex manifolds 18 Actions of fine abelian groups D Sundararaman C Kosniowski 46 Nonlinear problems of analysis in 19 Closed graph theorems and webbed spaces geometry and mechanics MDeWilde M Atteia, D Bancel and I Gumowski 20 Singular perturbation techniques applied to 47 Algorithmic methods in optimal control integro-differential equations W A Gruver and E Sachs H Grabmiiller 48 Abstract Cauchy problems and 21 Retarded functional differential equations: functional differential equations A global point of view F Kappel and W Schappacher S EA Mohammed 49 Sequence spaces 22 Multi parameter spectral theory in Hilbert space WHRuckle BDSleeman 50 Recent contributions to nonlinear 24 Mathematical modelling techniques partial differential equations RAris H Berestycki and H Brezis 25 Singular points of smooth mappings 51 Subnormal operators CG Gibson JBConway 26 Nonlinear evolution equations solvable by the 52 Wave propagation in viscoelastic media spectral transform FMainardi FCalogero 53 Nonlinear partial differential equations and 27 Nonlinear analysis and mechanics: their applications: College de France Heriot-Watt Symposium Volume II Seminar. Volume I RJKnops H Brezis and J L Lions 54 Geometry of Coxeter groups 79 Free boundary problems, theory and H Hiller applications. Volume II 55 Cusps of Gauss mappings A Fasano and M Primicerio T Banchoff, T Gaffney and C McCrory 80 Symplectic geometry 56 An approach to algebraic K-theory A Crumeyrolle and J Grifone AJBerrick 81 An algorithmic analysis of a communication 57 Convex analysis and optimization model with retransmission of flawed messages J-P Aubin and RB Vintner D M Lucantoni 58 Convex analysis with applications in 82 Geometric games and their applications the differentiation of convex functions WHRuckle JR Giles 83 Additive groups of rings 59 Weak and variational methods for moving S Feigelstock boundary problems 84 Nonlinear partial differential equations and C M Elliott and J R Ockendon their applications: College de France 60 Nonlinear partial differential equations and Seminar. Volume IV their applications: College de France H Brezis and J L Lions Seminar. Volume II 85 Multiplicative functionals on topological algebras H Brezis and J L Lions THusain 61 Singular systems of differential equations II 86 Hamilton-Jacobi equations in Hilbert spaces SL Campbell V Barbu and G Da Prato 62 Rates of convergence in the central limit 87 Harmonic maps with symmetry, harmonic theorem morphisms and deformations of metrics Peter Hall PBaird 63 Solution of differential equations 88 Similarity solutions of nonlinear partial by means of one-parameter groups differential equations J MHill LDresner 64 Hankel operators on Hilbert space 89 Contributions to nonlinear partial differential SC Power equations 65 Schrodinger-type operators with continuous C Bardos, A Damlamian, J I Diaz and spectra J Hernandez M S P Eastham and H Kalf 90 Banach and Hilbert spaces of vector-valued 66 Recent applications of generalized inverses functions SL Campbell J Burbea and P Masani 67 Riesz and Fredholm theory in Banach algebra 91 Control and observation of neutral systems BA Barnes, G J Murphy, MR F Smyth and DSalamon T TWest 92 Banach bundles, Banach modules and 68 Evolution equations and their applications automorphisms of C*-algebras F Kappel and W Schappacher M J Dupre and R M Gillette 69 Generalized solutions of Hamilton-Jacobi 93 Nonlinear partial differential equations and equations their applications: College de France PL Lions Seminar. Volume V 70 Nonlinear partial differential equations and H Brezis and J L Lions their applications: College de France Seminar. 94 Computer algebra in applied mathematics: Volume III an introduction to MACSYMA H Brezis and J L Lions RH Rand 71 Spectral theory and wave operators for the 95 Advances in nonlinear waves. Volume I Schrodinger equation LDebnath A MBerthier 96 FC-groups 72 Approximation of Hilbert space operators I M J Tomkinson DA Herrero 97 Topics in relaxation and ellipsoidal methods 73 Vector valued Nevanlinna Theory M Akgiil HJWZiegler 98 Analogue of the group algebra for 74 Instability, nonexistence and weighted topological semigroups energy methods in fluid dynamics H Dzinotyiweyi and related theories 99 Stochastic functiona-l differential equations BStraughan S EA Mohammed 75 Local bifurcation and symmetry 100 Optimal control of variational inequalities A Vanderbauwhede VBarbu 76 Clifford analysis 101 Partial differential equations and F Brackx, R Delanghe and F Sommen dynamical systems 77 Nonlinear equivalence, reduction of PD Es W E Fitzgibbon III to OD Es and fast convergent numerical 102 Approximation of Hilbert space operators. methods Volume II EE Rosinger C Apostol, LA Fialkow, DA Herrero and 78 Free boundary problems, theory and D Voiculescu applications. Volume I 103 Nondiscrete induction and iterative processes A Fasano and M Primicerio V Ptak and F-A Potra ABOUT THIS VOLUME The 1984/85 symposium on Stochastic Differential Equations and Applicd'lions held at Warwick University was designed to emphasize the interactions of stochastic analysis with other branches of mathema'fics, particularly differential geometry, and with mathematical physics. This volume consists of articles emanating from that symposium and shows the fruitfulness of those interactions. Topics involved include classical and quantum probability theory, differential analysis in infinite dimensions, potential theory, stochastic control, index theorems, stochastic mechanics, analysis on manifolds, and Lorentz geometry. The articles contain careful expositions as well as giving the latest results, so the volume will provide the reader who has some knowledge of stochastic analysis with an introduction to its various roles and to the mathematical baQkground needed to understand both its potential uses and how the problems ati ina from its varied applications have, in their turn, shaped the general theory. Reudershlp: Researchers and graduate students in mathematics, mathematical physics and probability theory. PITMAN RESEARCH NOTES IN MATHEMATICS SERIES The aim of this series is to disseminate important new material of a specialist nature in economic form. It ranges over the whole spectrum of mathematics and also reflects the changing momentum of dialogue between hitherto distinct areas of pure and applied parts of the discipline. The editorial board has been chosen accordingly and will from time to time be recompo,sed to represent the full diversity of mathematics as covered by Mathematical Reviews. · This is a rapid means of publication for current material whose style of exposition is that of a developing subject. Work that is in most respects final and definitive, but not yet'tefined into a formal monograph, will also be considered for a place in the series. Normally homogeneous material is required, even if written by more than one author, thus multi-author works will be included provided that there is a strong linking theme or editorial pattern. Proposals and manuscripts: See inside book. 104 Analytic functions - growth aspects 130 Stochastic differential equations 0 P Juneja and G P Kapoor RWu 105 Theory ofTikhonov regularization for 131 Differential geometry Fredholm equations of the first kind LA Cordero CW Groetsch 132 Nonlinear differential equations 106 Nonlinear partial differential equations and free J K Hale and P Martinez-Amores boundaries. Volume I 133 Approximation theory and applications JI Diaz SP Singh 107 Tight and taut immersions of manifolds 134 Near-rings and their links with groups T E Cecil and P J Ryan JDPMeldrum 108 A layering method for viscous, incompressible 135 Estimating eigenvalues with a posteriori/a priori L1, flows occupying R" inequalities A Douglis and E B Fabes J R Kuttler and V G Sigillito 109 Nonlinear partial differential equations and 136 Regular semigroups as extensions their applications: College de France F J Pastijn and M Petrich Seminar. Volume VI 137 Representations of rank one Lie groups H Brezis and J L Lions D H Collingwood 110 Finite generalized quadrangles 138 Fractional calculus S E Payne and J A Thas G F Roach and AC McBride Ill Advances in nonlinear waves. Volume II 139 Hamilton's principle in LDebnath continuum mechanics 112 Topics in several complex variables A Bedford E Ramirez de Arellano and D Sundararaman 140 Numerical analysis 113 Differential equations, flow invariance and D F Griffiths and G A Watson applications 141 Semigroups, theory and applications. Volume I NH Pavel H Brezis, M G Crandall and F Kappel 114 Geometrical combinatorics 142 Distribution theorems of L-functions F C Holroyd and R J Wilson DJoyner 115 Generators of strongly continuous semigroups 143 Recent developments in structured continua J A van Casteren D De Kee and P Kaloni 116 Growth of algebras and Gelfand-Kirillov 144 Functional analysis and two-point differential dimension operators G R Krause and T H Lenagan JLocker 117 Theory of bases and cones 145 Numerical methods for partial differential PK Kamthan and M Gupta equations 118 Linear groups and permutations S I Hariharan and T H Moulden A R Camina and EA Whelan 146 Completely bounded maps and dilations 119 General Wiener-Hopf factorization methods VI Paulsen F-OSpeck 147 Harmonic analysis on the Heisenberg nilpotent 120 Free boundary problems: applications and Lie group theory, Volume Ill WSchempp A Bossavit, A Damlamian and M Fremond 148 Contributions to modern calculus of variations 121 Free boundary problems: applications and LCesari theory, Volume IV 149 Nonlinear pa'rabolic equations: qualitative A Bossavit, A Damlamian and M Fremond properties of solutions 122 Nonlinear partial differential equations and L Boccardo and A Tesei their applications: College de France 150 From local times to global geometry, control and Seminar. Volume VII physics H Brezis and J L Lio,ns KDElworthy 123 Geometric methods in operator algebras 151 A stochastic maximum principle for optimal H Araki and E G Effros control of diffusions 124 Infinite dimensional analysis-stochastic U G Haussmann processes 152 Semigroups, theory and applications. Volume II S Albeverio H B1·ezis, M G Crandall and F Kappel 125 Ennio de Giorgi Colloquium PKree 126 Almost-periodic functions in abstract spaces SZaidman 127 Nonlinear variational problems A Marino, L Modica, S Spagnolo and M Degiovanni 128 Second-order systems of partial differential equations in the plane L K Hua, W Lin and C-Q Wu 129 Asymptotics of high-order ordinary differential equations RB Paris and AD Wood From local times to global geometry, control and physics K D Elworthy (Editor) University of Warwick From local times to global geometry, control and physics Emanations from the Warwick Symposium on Stochastic Differential Equations and Applications, 1984/85 ... .-. ... Longman """""" Scientific & h . 1 ._........... 'TJl. ec nica Copublished in the United States with John Wiley & Sons, Inc., New York