Examples of random fields that can be represented as space-domain scaled stationary Ornstein-Uhlenbeck fields
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Mátyás Barczy
Abstract
We give some examples of random fields that can be represented as space-domain scaled stationary Ornstein-Uhlenbeck fields defined on the plane. Namely, we study a tied-down Wiener bridge, tied-down scaled Wiener bridges, a Kiefer process and so called (F, G)-Wiener bridges.
Acknowledgement
I would like to thank Endre Iglói and Peter Kern for giving useful comments on the paper. I am undoubtedly grateful to the referee for his/her valuable comments that have led to an improvement of the manuscript.
References
[1] Baran, S.—Pap, G.—van Zuijlen, M. C. A.: Estimation of the mean of stationary and nonstationary Ornstein-Uhlenbeck processes and sheets, Comput. Math. Appl. 45 (2003), 563–579.10.1016/S0898-1221(03)00017-8Suche in Google Scholar
[2] Barczy, M.—Iglói, E.}: Karhunen-Loéve expansions of alpha-Wiener bridges, Cent. Eur. J. Math. 9 (2011), 65–84.10.2478/s11533-010-0090-8Suche in Google Scholar
[3] Barczy, M.—Kern, P.: Gauss-Markov processes as space-time scaled stationary Ornstein-Uhlenbeck processes, (2014), available at https://arxiv.org/abs/1409.7253v2.Suche in Google Scholar
[4] Brennan, M. J.—Schwartz, E. S.: Arbitrage in stock index futures, Journal of Business 63 (1990), 7–31.10.1086/296491Suche in Google Scholar
[5] Csörgő M.—Révész P.: Strong Approximations in Probability and Statistics, Academic Press, New York, 1981.Suche in Google Scholar
[6] Deheuvels, P.—Peccati, G.—Yor, M.: On quadratic functionals of the Brownian sheet and related processes, Stochastic Process. Appl. 116 (2006), 493–538.10.1016/j.spa.2005.10.004Suche in Google Scholar
[7] Doob, J. L.: The Brownian movement and stochastic equations, Ann. of Math. 43 (1942), 351–369.10.2307/1968873Suche in Google Scholar
[8] Khmaladze, E.: Unitary transformations, empirical processes and distribution free testing, Bernoulli 22 (2016), 563–588.10.3150/14-BEJ668Suche in Google Scholar
[9] Lamperti, J.: Semi-stable stochastic processes, Trans. Amer. Math. Soc. 104 (1962), 62–78.10.1090/S0002-9947-1962-0138128-7Suche in Google Scholar
[10] Mansuy, R.: On a one-parameter generalization of the Brownian bridge and associated quadratic functionals, J. Theoret. Probab. 17 (2004), 1021–1029.10.1007/s10959-004-0588-8Suche in Google Scholar
[11] Shorack, G. R.—Wellner, J. A.: Empirical Processes with Applications to Statistics, John Wiley & Sons, Inc., 1986.Suche in Google Scholar
[12] van der Vaart, A. W.: Asymptotic Statistics, Cambridge University Press, Cambridge, 1998.10.1017/CBO9780511802256Suche in Google Scholar
[13] Walsh, J. B.: An introduction to stochastic partial differential equations. In: École d’été de probabilités de Saint-Flour, XIV-1984, Lecture Notes in Math. 1180, Springer, Berlin, 1986, pp. 265–439.10.1007/BFb0074920Suche in Google Scholar
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- On the number of cycles in a graph
- Characterization of posets for order-convergence being topological
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