On Weak Convergence of Stochastic Processes with Multidimensional Time Parameter

On $L_1$-weak ergodicity of nonhomogeneous continuous-time Markov‎ ‎processes

‎In the present paper we investigate the $L_1$-weak ergodicity of‎ ‎nonhomogeneous continuous-time Markov processes with general state‎ ‎spaces‎. ‎We provide a necessary and sufficient condition for such‎ ‎processes to satisfy the $L_1$-weak ergodicity‎. ‎Moreover‎, ‎we apply‎ ‎the obtained results to establish $L_1$-weak ergodicity of quadratic‎ ‎stochastic processes‎.

Weak Convergence of Stochastic Processes Defined on Semi-infinite Time Intervals

In the standard theorems on weak convergence of stochastic processes, it is invariably assumed that the parameter set is a bounded interval. The object of this paper is to indicate that analogues of these theorems for unbounded intervals are also valid. We shall confine our attention to the results of Skorohod [l], and in particular to those results concerning his Ji topology. Let £ be a comple...

On Convergence of Stochastic Processes

where £iX) is the distribution function of the random variable X,f( ) is a real-valued function 5 continuous almost everywhere (p), and the limit is in the sense of the usual weak convergence of distributions. Equation (2) is usually the real center of interest, for many " limit-distribution theorems" are implicit in it. It is clear that for given {pn} and p, the better theorem of this kind wou...

@bullet , @bullet Weak Convergence of Multidimensional Empirical Processes for Stationary ¢-mixing Processes

Comment on “Weak Convergence to a Matrix Stochastic Integral with Stable Processes”

In this paper we identify a lacuna in a proof in the paper by M. Caner published in 1997 in this Journal concerning the weak limit behavior of various expressions involving heavy-tailed multivariate vectors and the convergence of stochastic integrals. In a later paper (Caner, 1998) uses results for these limit relations to formulate tests for cointegration with infinite variance errors.