Distributional and entire solutions of ordinary differential and functional differential equations.
Shah, S.M., Wiener, Joseph (1983)
International Journal of Mathematics and Mathematical Sciences
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Shah, S.M., Wiener, Joseph (1983)
International Journal of Mathematics and Mathematical Sciences
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Mátyás Barczy, Endre Iglói (2011)
Open Mathematics
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We study Karhunen-Loève expansions of the process(X t(α))t∈[0,T) given by the stochastic differential equation , with the initial condition X 0(α) = 0, where α > 0, T ∈ (0, ∞), and (B t)t≥0 is a standard Wiener process. This process is called an α-Wiener bridge or a scaled Brownian bridge, and in the special case of α = 1 the usual Wiener bridge. We present weighted and unweighted Karhunen-Loève expansions of X (α). As applications, we calculate the Laplace transform and the distribution...
Giovanni Peccati, Marc Yor (2006)
Banach Center Publications
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We present three new identities in law for quadratic functionals of conditioned bivariate Gaussian processes. In particular, our results provide a two-parameter generalization of a celebrated identity in law, involving the path variance of a Brownian bridge, due to Watson (1961). The proof is based on ideas from a recent note by J.-R. Pycke (2005) and on the stochastic Fubini theorem for general Gaussian measures proved in Deheuvels et al. (2004).
Mireille Chaleyat-Maurel, David Nualart (1995)
Séminaire de probabilités de Strasbourg
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Pawan Kumar Kamthan (1965-1966)
Compositio Mathematica
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J. Soler (1980)
Banach Center Publications
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Martin T. Barlow, Peter Imkeller (1992)
Séminaire de probabilités de Strasbourg
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Wiener, Joseph (1982)
International Journal of Mathematics and Mathematical Sciences
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Fricke, G.H., Roy, Ranjan, Shah, S.M. (1981)
International Journal of Mathematics and Mathematical Sciences
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Perrin, O., Zani, M. (2005)
Zapiski Nauchnykh Seminarov POMI
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Wang, Jun, Laine, Ilpo (2009)
Abstract and Applied Analysis
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Bose, Anil K., Cover, Alan S., Reneke, James A. (1991)
International Journal of Mathematics and Mathematical Sciences
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