Nonnegative Supermartingales and Martingales, and the Girsanov Theorem
Let (Ω, F, P) be a complete probability space, and let (F t ), 0 ≤ t ≤ T, be a nondecreasing family of sub-σ-algebras of F, augmented by sets from F of probability zero. Let W = (W t , F t ) be a Wiener process and let γ = (γ t , F t ) be a random process
- PDF / 33,630,501 Bytes
- 434 Pages / 439.091 x 666.218 pts Page_size
- 97 Downloads / 184 Views
Applications of Mathematics Stochastic Modelling and Applied Probability
5
Edited by 1. Karatzas M.Yor
Advisory Board P. Bremaud
E.Carlen W. Fleming D. Geman G. Grimmett G. Papanicolaou J. Scheinkman
Springer-Verlag Berlin Heidelberg GmbH
Applications of Mathematics Fleming/Rishel, Deterministic and Stochastic Optimal Control (1975) 2 Marchuk, Methods of Numerical Mathematics (1975, 2nd. ed. 1982) 3 Balakrishnan, Applied Functional Analysis (1976, 2nd. ed. 1981) 4 Borovkov, Stochastic Processes in Queueing Theory (1976) 5 LiptserlShiryaev, Statistics of Random Processes I: General Theory (1977, 2nd. ed. 2001) 6 LiptserlShiryaev, Statistics of Random Processes II: Applications (1978, 2nd. ed. 2001) 7 Vorob'ev, Game Theory: Lectures for Economists and Systems Scientists (1977) 8 Shiryaev, Optimal Stopping Rules (1978) 9 Ibragimov/Rozanov, Gaussian Random Processes (1978) lOW onham, Linear Multivariable Control: A Geometric Approach (1974,3rd.ed.1985) 11 Hida, Brownian Motion (1980) 12 Hestenes, Conjugate Direction Methods in Optimization (1980) 13 Kallianpur, Stochastic Filtering Theory (1980) 14 Krylov, Controlled Diffusion Processes (1980) 15 Prabhu, Stochastic Storage Processes: Queues, Insurance Risk, and Dams (1980) 16 Ibragimov/Has'minskii, Statistical Estimation: Asymptotic Theory (1981) 17 Cesari, Optimization: Theory and Applications (1982) 18 Elliott, Stochastic Calculus and Applications (1982) 19 Marchuk/Shaidourov, Difference Methods and Their Extrapolations (1983) 20 Hijab, Stabilization of Control Systems (1986) 21 Protter, Stochastic Integration and Differential Equations (1990) 22 Benveniste/Metivier/Priouret, Adaptive Algorithms and Stochastic Approximations (1990) 23 Kloeden/Platen, Numerical Solution of Stochastic Differential Equations (1992, corr. 3rd. printing 1999) 24 Kushner/Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time (1992) 25 Fleming/Soner, Controlled Markov Processes and Viscosity Solutions (1993) 26 Baccelli/Bremaud, Elements of Queueing Theory (1994) 27 Winkler, Image Analysis, Random Fields and Dynamic Monte Carlo Methods (1995) 28 Kalpazidou, Cycle Representations of Markov Processes (1995) 29 Elliottl Aggoun/Moore, Hidden Markov Models: Estimation and Control (1995) 30 Hernandez-LermalLasserre, Discrete-Time Markov Control Processes (1995) 31 Devroye/Gyilrfi/Lugosi, A Probabilistic Theory of Pattern Recognition (1996) 32 MaitralSudderth, Discrete Gambling and Stochastic Games (1996) 33 Embrechts/Kliippelberg/Mikosch, Modelling Extremal Events for Insurance and Finance (1997, corr. 2nd printing 1999) 34 Duflo, Random Iterative Models (1997) 35 KushnerlYin, Stochastic Approximation Algorithms and Applications (1997) 36 Musiela/Rutkowski, Martingale Methods in Financial Modelling (1997) 37 Yin, Continuous-Time Markov Chains and Applications (1998) 38 Dembo/Zeitouni, Large Deviations Techniques and Applications (1998) 39 Karatzas, Methods of Mathematical Finance (1998) 40 Fayolle/lasnogorodski/Malyshev, Random Walks in the Quarter-Plane (1999) 41 Ave
