A p-stable limit theorem holds for partial sums Sn of a stationary sequence, if Sn/Bn -- g[mu] for some 1/p-regularly varying sequence and some non-denegerate strictly p-stable law [mu]. The case 0 p 2 is investigated in detail and simplified necessary and sufficient conditions are given. The...

Let v(A) be the extinction probability for a contact process on a countable set S with initial state A [subset of] S. We prove that for any sets A, B [subset of] S, [nu](A[intersection]B)[nu](A[union or logical sum]B)[greater-or-equal, slanted][nu](A)[nu](B). We also prove an analogous statement...

Bahadur-Kiefer approximations for generalized quantile processes as defined in Einmahl and Mason (1992) are given which generalize results for the classical one-dimensional quantile processes. An as application we consider the special case of the volume process of minimum volume sets in classes...

Let x(t) be a one-dimensional Brownian motion. The homing problem for a controlled x(t) process is solved by using a mathematical expectation for an uncontrolled geometric Brownian motion. Furthermore, it turns out that the optimally controlled process is a Bessel process. Similarly, a geometric...

We consider recursions of the form xn + 1 = [phi]n[xn], where {[phi]n, n = 0} is a stationary ergodic sequence of maps from a Polish space (E, ) into itself, and {xn, n = 0} are random variables taking values in (E, ). Questions of existence and uniqueness of stationary solutions are of...

In this paper we establish the existence and uniqueness of a solution for stochastic Volterra equations assuming that the coefficients F(t,s,x) and Gi(t,s,x) are Ft-measurable, for s[less-than-or-equals, slant]t, where {Ft} denotes the filtration generated by the driving Brownian motion. We...

Asymptotically maximum likelihood estimators and estimators asymptotically minimizing criterial functions of observations are considered in statistical models with generalized sequences of observations. New necessary and sufficient conditions for consistency of these estimators are established....

We study stability with respect to perturbation of coefficients and existence of weak solutions of stochastic differential equations with reflecting boundary conditions. We assume that the domain is a convex subset of d or satisfies quite general conditions introduced by Lions and Sznitman. The...

Second-order regular variation is a refinement of the concept of regular variation which is useful for studying rates of convergence in extreme value theory and asymptotic normality of tail estimators. For a distribution tail 1 - F which possesses second-order regular variation, we discuss how...

For backward stochastic differential equation (BSDE) with jumps and with non-Lipschitzian coefficient the existence and uniqueness of an adapted solution is obtained. By generalizing the existence result on partial differential and integral equations (PDIE) and Ito formula to the functions with...