Abstract
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 with
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Bibliography
Notes and References. 1
Novikov, A.A. (1972): On an identity for stochastic integrals. Teor. Veroyatn. Primen., 17, 4, 761 - 5
Gikhman, I.I. and Skorokhod, A.V. (1980): Stochastic Differential Equations. Springer-Verlag, Berlin Heidelberg New York
Girsanov, I.V. (1960): On transformation of one class of random processes with the help of absolutely continuous change of the measure. Teor. Veroyatn. Primen., 5, 1, 314 - 30
Liptser, R.S. and Shiryaev, A.N. (1972): On absolute continuity of measures corresponding to diffusion type processes with respect to a Wiener measure. Izv. Akad. Nauk SSSR, Ser. Mat., 36, 4, 874 - 89
Notes and References.2
Karatzas, I. and Shreve, S.E. (1991): Brownian Motion and Stochastic Calculus. Springer-Verlag, New York Berl in Heidelberg
Shiryaev, A.N. (1999): Essentials of Stochastic Finance. World Scientific, Singapore
Jacod, J. and Shiryaev, A.N. (1987): Limit Theorems for Stochastic Processes. Springer-Verlag, Berlin Heidelberg New York
Liptser, R.S. and Shiryaev, A.N. (1989): Theory of Martingales. Kluwer, Dordrecht (Russian edition 1986 )
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Liptser, R.S., Shiryaev, A.N. (2001). Nonnegative Supermartingales and Martingales, and the Girsanov Theorem. In: Statistics of Random Processes. Applications of Mathematics, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-13043-8_7
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DOI: https://doi.org/10.1007/978-3-662-13043-8_7
Publisher Name: Springer, Berlin, Heidelberg
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