Abstract
We prove that arbitrary Hunt processes on a general state space can be approximated by multivariate Poisson processes starting from each point of the state space. The key point is that no additional regularity assumption on the state space and on the underlying transition semigroup is used.
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Albeverio, S. and Röckner, M.: New developments in the theory and applications of Dirichlet forms, In: S. Albeverio et al.(eds), Stochastic Processes, Physics and Geometry, World Scientific, Singapore, 1990.
Deck, T., Potthoff, J. and Våge, G.: A review of white noise analysis from a probabilistic standpoint, Acta Appl. Math. 48(1997), 91–112.
Hida, T.: Analysis of Brownian Functionals, Carleton Math. Lecture Notes, No. 13, 1975.
Hida, T.: Brownian Motion, Springer, New York, 1980.
Hida, T., Kuo, H.-H., Potthoff, J. and Streit, L.: White Noise – An Infinite Dimensional Calculus, Kluwer Acad. Publ., Dordrecht, 1993.
Hille, E. and Phillips, R. S.: Functional Analysis and Semigroups, Amer. Math. Soc. Colloq. Publ., Amer. Math. Soc., Providence, 1957.
Karatzas, I. and Shreve, S. E.: Brownian Motion and Stochastic Calculus, Springer, New York, 1988.
Kondratiev, Yu. G., Leukert, P., Potthoff, J., Streit, L. and Westerkamp, W.: Generalized functionals on Gaussian spaces – the characterization theorem revisited, J. Funct. Anal. 141(1996), 301–318.
Kubo, I. and Takenaka, S.: Calculus on Gaussian white noise I, Proc. Japan Acad. 56 (1980), 376–380.
Kuo, H.-H.: Gaussian Measures in Banach Spaces, Springer, New York, 1975.
McKean, H. P., Jr.: Stochastic Integrals, Academic Press, New York, 1969.
Reed, M. and Simon, B.: Methods of Modern Mathematical Physics I: Functional Analysis, Academic Press, New York, 1972.
Reed, M. and Simon, B.: Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness, Academic Press, New York, 1975.
Revuz, D. and Yor, M.: Continuous Martingales and Brownian Motion, Springer, New York, 1991.
Sansone, G.: Orthogonal Functions, Robert Krieger Publ. Co., 1977.
Simon, B.:Distributions and their Hermite expansions, J. Math. Phys. 12(1971), 140–148.
Schwartz, L.: Radon Measures on Arbitrary Topological Vector Spaces and Cylindrical Measures, Oxford Univ. Press, London, 1973.
Trèves, F.: Topological Vector Spaces, Distributions and Kernels, Academic Press, New York, 1967.
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Ma, ZM.M., Sun, W. Approximation of Hunt Processes by Multivariate Poisson Processes. Acta Applicandae Mathematicae 63, 233–243 (2000). https://doi.org/10.1023/A:1010722309200
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DOI: https://doi.org/10.1023/A:1010722309200