Prokhorov distances under sublinear expectations are presented in the CLT and the functional CLT, and the convergence rates for them are obtained by the Lindeberg method. In particular, the obtained estimate in the functional CLT yields the known Borovkov estimate in the classical functional CLT with an explicit constant.
We consider a random walk on a multidimensional integer lattice with random bounds on local times, conditioned on the event that it hits a high level before its death. We introduce an auxiliary "core" process that has a regenerative structure and plays a key role in our analysis. We obtain a number of representations for the distribution of the random walk in terms of the similar distribution of the "core" process. Based on that, we prove a number of limiting results by letting the high level to tend to infinity. In particular, we generalise results for a simple symmetric one-dimensional random walk obtained earlier in the paper by Benjamini and Berestycki (2010).
We investigate a linear regression model with one unknown parameter.The idea of recursive regression residuals is to estimate the regression parameter at each moment on the base of previous variables.Therefore the distribution of recursive residuals does not depend on the parameter.We investigate conditions for the weak convergence of the process of sums of recursive residuals, properly normalized, to a standard Wiener process.We obtain new conditions, which are better than ones in Sen (1982).The recursive residuals were introduced by Brown, Durbin and Evans (1975).Such residuals are the useful instrument for testing hypotheses about linear regression.Our results give opportunity to use correctly recursive residuals for a wide class of regression sequences, including sinusoidal and i.i.d.bounded.
Lundberg-type inequalities for ruin probabilities of non-homogeneous risk models are presented in this paper. By employing martingale method, the upper bounds of ruin probabilities are obtained for the general risk models under weak assumptions. In addition, several risk models, including the newly defined united risk model and quasi-periodic risk model with interest rate, are studied.
We analyse a Markov chain and perturbations of the transition probability and the one-step cost function (possibly unbounded) defined on it. Under certain conditions, of Lyapunov and Harris type, we obtain new estimates of the effects of such perturbation
'/%3e%3cuse xlink:href='%23a' transform='rotate(23.036 .093 25.536)'/%3e%3cuse xlink:href='%23a' transform='rotate(45.87 1.273 16.18)'/%3e%3cuse xlink:href='%23a' transform='rotate(69.945 .996 12.078)'/%3e%3cuse xlink:href='%23a' transform='rotate(20.66 -19.689 31.932)'/%3e%3c/svg%3e)
'%3e%3cpath fill='%23012169' d='M0 0v30h60V0z'/%3e%3cpath stroke='%23fff' stroke-width='6' d='m0 0 60 30m0-30L0 30'/%3e%3cpath stroke='%23C8102E' stroke-width='4' d='m0 0 60 30m0-30L0 30' clip-path='url(%23b)'/%3e%3cpath stroke='%23fff' stroke-width='10' d='M30 0v30M0 15h60'/%3e%3cpath stroke='%23C8102E' stroke-width='6' d='M30 0v30M0 15h60'/%3e%3c/g%3e%3c/svg%3e)