Analogues of Conditional Wiener Integrals with Drift and Initial Distribution on a Function Space

Dong Hyun Cho

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: Let C[0, T] denote a generalized Wiener space, the space of real‐valued continuous functions on the interval [0, T], and define a stochastic process Z:C[00,T]×[,T]→R by Z(x,t)=∫0t h(u)dx(u)+x(0)+a(t), for x ∈ C[0, T] and t ∈ [0, T], where h ∈ L2[0, T] with h ≠ 0 a.e. and a is a continuous function on [0, T]. Let Zn:C[0,T]→Rn+1 and Zn+1:C[0,T]→Rn+2 be given by Zn(x) = (Z(x, t0), Z(x, t1), …, Z(x, tn)) and Zn+1(x) = (Z(x, t0), Z(x, t1), …, Z(x, tn), Z(x, tn+1)), where 0 = t0

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:916423

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