We consider the determination of the optimal singular stochastic control for maximizing the expected cumulative revenue flows in the presence of a state-dependent marginal yield measuring the instantaneous returns accrued from irreversibly exerting the singular policy. As in standard models of...

The class of stochastic processes is characterized which, as multiplicative noise with large intensity, stabilizes a linear system with companion form dxd-matrix. This includes the characterization of parametric noise which stabilizes the damped inverse pendulum. The proof yields also an...

A general model of an optimal equivalent change of measure is considered. Existence and uniqueness conditions of a solution of backward semimartingale equation for the value process are given. This result is applied to determine the maximum price of a contingent claim.

Let {Xn, n[greater-or-equal, slanted]0} be a sequence of random variables on the probability space ([Omega],F,P) taking values in the alphabet S={1,2,...,N}, and Q be another probability measure on F, under which {Xn, n[greater-or-equal, slanted]0} is a Markov chain. Let h(P Q) be the sample...

We study the two-type Richardson model on , d[greater-or-equal, slanted]2, in the asymmetric case where the two particle types have different infection rates. Starting with a single particle of each type, and fixing the infection rate for one of the types, we show that mutual unbounded growth...

In the first part, we establish an upper bound of an iterated logarithm law for a sequence of processes endowed with the uniform convergence on compacts, where Mn(x) is a square integrable martingale for each x in . In the second part we present an iterative kernel estimator of the driving...

In a recent paper, Mokkadem (1997. Stoch. Proc. Appl. 72, 145-149) derived a simple test for randomness against ARMA alternatives. In this note we consider a transformation of the corresponding statistic and present an alternative proof of this result. Through this approach it is demonstrated...

Given an infinite sequence t=([var epsilon]k)k of -1 and +1, we consider the oriented walk defined by Sn(t)=[summation operator]k=1n[var epsilon]1[var epsilon]2...[var epsilon]k. The set of t's whose behaviors satisfy Sn(t)~bn[tau] is considered ( and 0[tau][less-than-or-equals, slant]1 being...

We present a new approximation theorem for estimating the error in approximating the whole distribution of a finite-point process by a suitable Poisson process. The metric used for this purpose regards the distributions as close if there are couplings of the processes with the expected average...

The following integral equation is considered:where g[set membership, variant]L1[reverse not equivalent]L1(-[infinity],[infinity]), dF is a Borel probability measure, possessing nonzero absolute continuous component; at least one of numbers [nu]±+[infinity] and [nu][not equal to]0, whereIt is...