Study of Dependence for Some Stochastic Processes ∗ Tomasz R. Bielecki † , Andrea Vidozzi ‡ , Luca Vidozzi § Department of Applied Mathematics Illinois Institute of Technology Chicago, IL 60616, USA Jacek Jakubowski ¶ Institute of Mathematics University of Warsaw 02-097 Warszawa, Poland Abstract The paper is concerned with studying the following problem: Consider a multivariate sto- chastic 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. * This research was supported in part by NSF Grants 0202851 and 0604789, and by Moody’s Corporation grant 5-55411. † Corresponding author; e-mail: bielecki@iit.edu ‡ e-mail: hemellos75@yahoo.com § e-mail: hemellos75@yahoo.com ¶ e-mail: jakub@mimuw.edu.pl 1