Weak convergence of stochastic integrals driven by martingale measure

Nhansook Cho

Stochastic Processes and their Applications, 1995, vol. 59, issue 1, 55-79

Abstract: Let be the dual of Schwartz space, , {Mn} be a sequence of martingale measures and let F be some suitable function space such as , , p [greater-or-equal, slanted] 2 or . We find conditions under which (Xn, Mn) => (X, M) in the Skorohod topology in implies [integral operator] Xn(x, s)Mn(dx, ds) => [integral operator] X(x, s) M(dx, ds) in the Skorohod topology in . We use the idea of regularization to reduce to a metrizable subspace in order to apply the Skorohod representation theorem and then appropriate the randomized mapping constructed by Kurtz and Protter to get step functions approximating the integrands. Using this result, we prove weak convergence of certain double stochastic integrals studied by Walsh. Let , {[eta]n} be a sequence of Brownian density processes and {Wn} and {Zn} be two sequences of martingale measures generated by particle systems. We consider the weak convergence of [integral operator] [empty set](x, y)[eta]ns(dx)Wn(dx, dy) and [integral operator] [empty set](x, y)[eta]ns(dx)Zn(dx, dy).

Keywords: Stochastic; integrals; Martingale; measures; Weak; convergence; Skorohod; topology; Brownian; density; process (search for similar items in EconPapers)
Date: 1995
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Citations: View citations in EconPapers (3)

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