论文信息 - Almost surely continuous solutions of a nonlinear stochastic integral equation

Almost surely continuous solutions of a nonlinear stochastic integral equation

A nonlinear stochastic integral equation of the Hammerstein type in the formx(t; ω) = h(t, x(t; ω)) + ∫sk(t, s; ω)f(s, x(s; ω); ω)dμ(s) is studied wheret ∈ S, a measure space with certain properties,ω ∈ Ω, the supporting set of a probability measure space (Ω,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.

W. J. Padgett | W. J. Padgett | William J. Padgett

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