For all p[greater-or-equal, slanted]1 let Mp(X1,...,Xn) denote the length of the minimal spanning tree through random variables X1,...,Xn, where the cost of an edge (Xi, Xj) is given by Xi-Xjp. If the Xi, i[greater-or-equal, slanted]1, are i.i.d. with values in [0,1]d, d[greater-or-equal,...

In this paper we derive a formula for zero-avoiding transition probabilities of an r-node tandem queue with exponential servers and deterministic input. In particular, we show that these transition probabilities may be interpreted as non-coincidence probabilities of a set of dissimilar Poisson...

We consider optimal stopping of independent sequences. Assuming that the corresponding imbedded planar point processes converge to a Poisson process we introduce some additional conditions which allow to approximate the optimal stopping problem of the discrete time sequence by the optimal...

Let X be the solution of an Itô differential equation with jumps over . Under some auxiliary assumptions on the parameters of the equation, we characterize the support of the law of X in the Skorohod space as the closure of the set of solutions to piecewise ordinary differential equations. This...

Our main intention is to describe the behavior of the (cumulative) distribution function of the random variable M0,1 := sup0[less-than-or-equals, slant]s,t[less-than-or-equals, slant]1 W(s,t) near 0, where W denotes one-dimensional, two-parameter Brownian sheet. A remarkable result of Florit and...

In this paper we transfer martingale representation theorems from some given filtration to an initially enlarged filtration , where G is a random variable satisfying an equivalence assumption. We use then one of these theorems to solve the problem of maximizing the expected utility from both...

A weighted embedding for the generalized pontogram {Kn(t): 0[less-than-or-equals, slant]t[less-than-or-equals, slant]1} corresponding pointwise to a renewal process {N(s): 0[less-than-or-equals, slant]s[infinity]} via Kn(t)=n-1/2(N(nt)-tN(n)) is studied in this paper. After proper normalization,...

Keilson (1979, Markov Chain Models -- Rarity and Exponentiality, Springer, New York) and Aldous (1989, Probability approximations via the Poisson Clumping Heuristic, Springer, New York) have given expressions for the asymptotics of the mean time until a rare event occurs. Here we extend these...

Solvability of forward-backward stochastic differential equations with nonsmooth coefficients is considered using the Four-Step Scheme and some approximation arguments. For the one-dimensional case, the existence of an adapted solution is established for the equation which allows the diffusion...

We prove existence, uniqueness and comparison theorems for a class of parabolic semilinear stochastic partial differential equations with nonlinearities of polynomial growth in the case of several space dimension.