Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$(X_1,X_2,\ldots ,X_n)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">(</mo> <msub> <mi>X</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>X</mi> <mn>2</mn> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>X</mi> <mi>n</mi> </msub> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> be a Gaussian random vector with a common correlation coefficient <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\rho _n,\,0\le \rho _n1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <msub> <mi mathvariant="italic">ρ</mi> <mi>n</mi> </msub> <mo>,</mo> <mspace width="0.166667em"/> <mn>0</mn> <mo>≤</mo> <msub> <mi mathvariant="italic">ρ</mi> <mi>n</mi> </msub> <mo></mo> <mn>1</mn> </mrow> </math> </EquationSource> </InlineEquation>, and let <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$M_n= \max (X_1,\ldots , X_n),\,n\ge 1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <msub> <mi>M</mi> <mi>n</mi> </msub> <mo>=</mo> <mo movablelimits="true">max</mo> <mrow> <mo stretchy="false">(</mo> <msub> <mi>X</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>X</mi> <mi>n</mi> </msub> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> <mspace width="0.166667em"/> <mi>n</mi>...</mo></mrow></math></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

We prove limit theorems for the super-replication cost of European options in a binomial model with friction. Examples covered are markets with proportional transaction costs and illiquid markets. A dual representation for the super-replication cost in these models is obtained and used to prove...

This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of the BSS model. We review the limit theory discussed in...

This paper presents the asymptotic theory for non-degenerate U-statistics of high frequency observations of continuous Itô semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the U-statistic. The...

We consider the problem of testing the null hypothesis of no change against the alternative of multiple change points in a series of independent observations. We propose an ANOVA-type test statistic and obtain its asymptotic null distribution. We also give approximations of its limiting critical...

We obtain limit theorems for a class of nonlinear discrete-time processes X(n) called the kth order Volterra processes of order k. These are moving average kth order polynomial forms: X(n)=∑0i1,…,ik∞a(i1,…,ik)ϵn−i1…ϵn−ik, where {ϵi} is i.i.d. with Eϵi=0, Eϵi2=1, where a(⋅)...