Almost surely continuous solutions of a nonlinear stochastic integral equation |
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Authors: | Padgett W. J. |
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Affiliation: | (1) Department of Mathematics and Computer Science, University of South Carolina, 29208 Columbia, S.C., USA |
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Abstract: | A nonlinear stochastic integral equation of the Hammerstein type in the formx(t; ) = h(t, x(t; )) + sk(t, s; )f(s, x(s; ); )d (s) is studied wheret S, a measure space with certain properties, , the supporting set of a probability measure space ( ,A, P), and the integral is a Bochner integral. A random solution of the equation is defined to be an almost surely continuousm-dimensional vector-valued stochastic process onS which is bounded with probability one for eacht S and which satisfies the equation almost surely. Several theorems are proved which give conditions such that a unique random solution exists.AMS (MOS) subject classifications (1970): Primary; 60H20, 45G99. Secondary: 60G99. |
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Keywords: | nonlinear stochastic integral equation stochastic Hammerstein equation random solution almost surely continuous processes |
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