ISSN:
1433-0490
Keywords:
nonlinear stochastic integral equation
;
stochastic Hammerstein equation
;
random solution
;
almost surely continuous processes
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
Notes:
Abstract A nonlinear stochastic integral equation of the Hammerstein type in the formx(t; ω) = h(t, x(t; ω)) + ∫ s k(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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01683263
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