With the df F of the rv X we associate the natural exponential family of df's F[lambda] wheredF[lambda](x)=e[lambda]x dF(x)/Ee[lambda]Xfor . Assume [lambda][infinity]=sup [Lambda][less-than-or-equals, slant][infinity] does not lie in [Lambda]. Let [lambda][short up arrow][lambda][infinity], then...

The topic of this paper is linear optimal prediction of hidden Markov models (HMMs) and innovations representations of HMMs. Our interest in these topics primarily arise from subspace estimation methods, which are intrinsically linked to such representations. For HMMs, derivation of innovations...

A Poisson driven stochastic differential equation generates a semigroup of operators (Pt)t[greater-or-equal, slanted]0 describing the evolution of measures along trajectories and a Markov operator P corresponding to the change of measures from a jump to jump. We show that the semigroup...

Consider a completely asymmetric Lévy process X and let Z be X reflected at 0 and at a0. In applied probability (e.g. The Single Server Queue, 2nd Edition, North-Holland, Amsterdam, 1982) the process Z turns up in the study of the virtual waiting time in an M/G/1-queue with finite buffer a or...

The notion of d-set arises in the theory of function spaces and in fractal geometry. Geometrically self-similar sets are typical examples of d-sets. In this paper stable-like processes on d-sets are investigated, which include reflected stable processes in Euclidean domains as a special case....

We consider a symmetric diffusion corresponding to uniformly elliptic divergence form operator with reflection at the boundary of a domain satisfying the general conditions introduced by Lions and Sznitman. We prove that for each starting point inside the domain the diffusion is a Dirichlet...

We consider a nonlinear controlled stochastic evolution equation in a Hilbert space, with a Wiener process affecting the control, assuming Lipschitz conditions on the coefficients. We take a cost functional quadratic in the control term, but otherwise with general coefficients that may even take...

In this paper, we give necessary and sufficient conditions for a stationary sequence of random variables with values in a separable Hilbert space to satisfy the conditional central limit theorem introduced in Dedecker and Merlevède (Ann. Probab. 30 (2002) 1044-1081). As a consequence, this...

We determine the ultimate ruin probability and the Laplace transform of the distribution of the time to ruin in the classical risk model, where claims arrive according to a renewal process, with waiting times that are of phase-type, while the claims themselves follow a distribution with a...

We study the convergence in law in , as [epsilon]--0, of the family of continuous processes {I[eta][epsilon](f)}[epsilon]0 defined by the multiple integralswhere f is a deterministic function and {[eta][epsilon]}[epsilon]0 is a family of processes, with absolutely continuous paths, converging in...