WHVB 随机积分的性质及收敛定理.pdfVIP

______________________________________________________________________________________ WHVB ∗ , 730070, : [1]riemann (WHVB ). : Henstock : 0211.6 The properties and convergence theorem of WHVB Wang caishi Chen jinshu (College of Mathematics and Information Scince, Northwest Normal University, Lanzhou 730070, Gansu, China) Abstract: In this paper we shall discuss the properties and convergence theorem of the stochastic integration which can be defined by Riemann’s approach using non-uniform meshes base on the paper [1], 1 δ[0, 1] ,-(I, ξ)belated δ- I ∈ [ξ, ξ + δ (ξ)], ξ ∈ [0, 1], I = (a, b][0, 1] , -{(I , ξ ) : i = 1, 2...n}[0.1]belated i i δ-,(i)I [0, 1] , (ii)i, I ⊂ [ξ , ξ + δ (ξ )]. i i i i i 1:δ (ξ, ω) : [0, 1] × Ω → (0, 1)ξ ∈ [0, 1] ω ∈ Ω,δ, ξ ∈ [0, 1], ξ + δ (ξ, .). (Ω, F , {F }, P )S (ω) t ≥ 0, {ω ∈ Ω : S (ω ≤ t} ∈ F . S, T t t S ≤ T ≤ 1,ω ∈ ΩS (ω) ≤ T (ω) ≤ 1,[S, T ] (S, T ] = {(t, ω) : S (ω) t T (ω), S(ω) T (ω); S (ω) = t = T (ω), S(ω) = T (ω)} δ -{((S , T ], ξ ) : i = 1, 2n} [0, 1]δ- i i i (i) ∀i, (S , T ]ω ∈ Ω, (S (ω), T (ω)] : i = 1, 2, ...n[0, 1] i i i i ; (ii) ((S , T ], ξ ) belat