Collision local times, historical stochastic calculus, and competing superprocesses.
We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate p∈(1/2, 1] and to the left at rate 1−p, interacting by exclusion. In the initial state there is a finite region such that to the left of this region all sites are occupied and to the right of it all sites are empty. Under this initial state, the hydrodynamical limit of the process converges to the rarefaction fan of the associated Burgers equation. In particular suppose that the...
A recurrent graph has the infinite collision property if two independent random walks on , started at the same point, collide infinitely often a.s. We give a simple criterion in terms of Green functions for a graph to have this property, and use it to prove that a critical Galton–Watson tree with finite variance conditioned to survive, the incipient infinite cluster in with and the uniform spanning tree in all have the infinite collision property. For power-law combs and spherically symmetric...
Those who follow Harold Jeffreys in using improper priors together with likelihoods to determine posteriors have thought of the improper measures as probability measures of a deviant sort. This is a mistake. Probability measures are finite measures. Improper distributions generate σ-finite measures. (...)
The present paper is devoted to further development of commutative nonstationary field themes; the first studies in this area were performed by K. Kirchev and V. Zolotarev [4, 5]. In this paper a more complicated variant of commutative field with nonstationary rank 2, carrying into more general situation for correlation function is studied. A condition of consistency (see (7) below) for commutative field is placed in the basis of the method proposed in [4, 5] and developed in this paper. The following...
The system of Abel equations α(ft(x)) = α(x) + λ(t), t ∈ T, is studied under the general assumption that are pairwise commuting homeomorphisms of a real interval and have no fixed points (T is an arbitrary non-empty set). A result concerning embeddability of rational iteration groups in continuous groups is proved as a simple consequence of the obtained theorems.
* Partially supported by Grant MM-428/94 of MESC.In this paper we present some generalizations of results of M. S. Livšic [4,6], concerning regular colligations (A1, A2, H, Φ, E, σ1, σ2, γ, ˜γ) (σ1 > 0) of a pair of commuting nonselfadjoint operators A1, A2 with finite dimensional imaginary parts, their complete characteristic functions and a class Ω(σ1, σ2) of operator-functions W(x1, x2, z): E → E in the case of an inner function W(1, 0, z) of the class Ω(σ1). ...