Keywords
- Hilbert Space
- Brownian Motion
- Gaussian Measure
- Continuous Semigroup
- Infinitesimal Generator
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References
R.M. Anderson: A Nonstandard Representation of Brownian Motion and Itô Integration. Israel J. Math. 25 (1976) pp. 15–46.
R.M. Anderson: Star-finite Probability Theory. Ph.D.-thesis, Yale University, 1977.
A. Bensoussan and R. Teman: Equation aux Derivées Partielles Stochastiques, Israel J. Math. 11 (1972)
A. Chojnowska-Michalik: Stochastic Differential Equations in Hilbert Spaces, in Z. Ciesielski (ed): Probability Theory. Banach Center Publications, Vol. 5, PWN, 1979.
P.-L. Chow: Stochastic Partial Differential Equations in Turbulence Related Problems, in A.T. Bharucha-Reid (ed): Probabilistic Analysis and Related Topics 1, Academic Press 1978
L. Gross: Abstract Wiener Spaces, Proc. 5th. Berkeley Sym. Math. Stat. Prob. 2 (1965), pp 31–42.
H.J. Keisler: An Infinitesimal Approach to Stochastic Analysis, Preliminary Version, 1978. (To app. Mem. AMS)
H.-H. Kuo: Gaussian Measures in Banach Spaces, LNM 463, Springer-Verlag, 1975.
T.L. Lindstrøm: Hyperfinite Stochastic Integration I: The Nonstandard Theory. Math. Scand. 46, pp265–292.
T.L. Lindstrøm: Hyperfinite Stochastic Integration II: Comparison with the Standard Theory. Math. Scand. 46, pp293–324.
T.L. Lindstrøm: Hyperfinite Stochastic Integration III: Hyperfinite Representations of Standard Martingales. Math. Scand. 46 (1980), pp 315–332.
T.L. Lindstrøm: A Loeb-measure Approach to Theorems by Prohorov, Sazonov, and Gross. Trans AMS 269 (1982).
P.A. Loeb: An Introduction to Nonstandard Analysis and Hyperfinite Probability Theory, in A.T. Bharucha-Reid (ed): Probabilistic Analysis and Related Topics 2, Academic Press, 1979, pp 105–142.
E. Pardoux: Equations aux derivées partielles stochastiques monotones, C.R. Acad. Sci. Paris, Ser. A, 275(1972).
M. Reed and B. Simon: Methods of Modern Mathematical Physics II, Academic Press, 1975.
K.D. Stroyan and W.A.J. Luxemburg: Introduction to the Theory of Infinitesimals, Academic Press, 1976.
D.N. Hoover and E.A. Perkins: Nonstandard Construction of the Stochastic Integral and Applications to Stochastic Differential Equations, I–II, To appear Trans. AMS.
T.L. Lindstrøm: The Structure of Hyperfinite Stochastic Integrals. To appear Zeit. f. Wahr. Theorie.
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© 1983 Springer-Verlag
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Lindstrøm, T.L. (1983). Stochastic integration in hyperfinite dimensional linear spaces. In: Hurd, A.E. (eds) Nonstandard Analysis-Recent Developments. Lecture Notes in Mathematics, vol 983. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065338
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DOI: https://doi.org/10.1007/BFb0065338
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