Motivated by problems in functional data analysis, in this paper we prove the weak convergence of normalized partial sums of dependent random functions exhibiting a Bernoulli shift structure.

Assuming that {(Un,Vn)} is a sequence of càdlàg processes converging in distribution to (U,V) in the Skorohod topology, conditions are given under which {∬fn(β,u,v)dUndVn} converges weakly to ∬f(β,x,y)dUdV in the space C(R), where fn(β,u,v) is a sequence of “smooth” functions...

In this paper, we consider some families of one-dimensional locally infinitely divisible Markov processes {ηtϵ}0≤t≤T with frequent small jumps. For a smooth functional F(x[0,T]) on space D[0,T], the following asymptotic expansions for expectations are proved: as...

A parameterized family of financial market models is presented. These models have jumps intrinsic to the price processes yet have strict completeness, equivalent martingale measures, and no arbitrage. For each value of the parameter $\beta (-2\leq\beta 0)$ the model is just as rich as the...

We analyze the joint convergence of sequences of discounted stock prices and Radon-Nicodym derivatives of the minimal martingale measure when interest rates are stochastic. Therefrom we deduce the convergence of option values in either complete or incomplete markets. We illustrate the general...