Study of Dependence for Some Stochastic Processes
by Tomasz Bielecki of the Illinois Institute of Technology,
August 14, 2007
Abstract: The paper is concerned with studying the following problem: Consider a multivariate stochastic process whose law is characterized in terms of some infinitesimal characteristics, such as the infinitesimal generator in case of finite Markov chains. Under what conditions imposed on these infinitesimal characteristics of this multivariate process, the univariate components of the process agree in law with given univariate stochastic processes. Thus, in a sense, we study a stochastic processes' counterpart of the stochastic dependence problem, which in case of real valued random variables is solved in terms of Sklar's theorem. The theory originated in the paper was motivated by potential applications to valuation and hedging of multi-name credit products.
Published in: Stochastic Analysis and Applications, Vol. 26, No. 4, (July 2008), pp. 903-924.
Previously titled: Study of Dependence for Some Classes of Stochastic Processes