An almost sure scaling limit theorem for Dawson-Watanabe superprocesses

We establish a scaling limit theorem for a large class of Dawson-Watanabe superprocesses whose underlying spatial motions are symmetric Hunt processes, where the convergence is in the sense of convergence in probability. When the underling process is a symmetric diffusion with -coefficients or a symmetric Lévy process on Rd whose Lévy exponent Ψ(η) is bounded from below by cα|η| for some c>0 and α∈(0,2) when |η| is large, a stronger almost sure limit theorem is established for the superprocess. Our approach uses the principal eigenvalue and the ground state for some associated Schrödinger operator. The limit theorems are established under the assumption that an associated Schrödinger operator has a spectral gap.     

Markov snakes and superprocesses

Summary We suggest the name Markov snakes for a class of path-valued Markov processes introduced recently by J.-F. Le Gall in connection with the theory of branching measure-valued processes. Le Gall applied this class to investigate path properties of superdiffusions and to approach probabilistically partial differential equations involving a nonlinear operator v–v ². We establish an isomorphism theorem which allows to translate results on continuous superprocesses into the language of Markov snakes and vice versa. By using this theorem, we get limit theorems for discrete Markov snakes.Partially supported by National Science Foundation Grant DMS-9301315 and by The US Army Research Office through the Mathematical Sciences Institute at Cornell University     

Light affine lambda calculus and polynomial time strong normalization

Light Linear Logic (LLL) and Intuitionistic Light Affine Logic (ILAL) are logics that capture polynomial time computation. It is known that every polynomial time function can be represented by a proof of these logics via the proofs-as-programs correspondence. Furthermore, there is a reduction strategy which normalizes a given proof in polynomial time. Given the latter polynomial time “weak” normalization theorem, it is natural to ask whether a “strong” form of polynomial time normalization theorem holds or not. In this paper, we introduce an untyped term calculus, called Light Affine Lambda Calculus (λLA), which corresponds to ILAL. λLA is a bi-modal λ-calculus with certain constraints, endowed with very simple reduction rules. The main property of LALC is the polynomial time strong normalization: any reduction strategy normalizes a given λLA term in a polynomial number of reduction steps, and indeed in polynomial time. Since proofs of ILAL are structurally representable by terms of λLA, we conclude that the same holds for ILAL. This is a full version of the paper [21] presented at LICS 2001.     

Path processes and historical superprocesses

Summary A superprocessX over a Markov process can be obtained by a passage to the limit from a branching particle system for which describes the motion of individual particles.The historical process for is the process whose state at timet is the path of over time interval [0,t]. The superprocess over the historical superprocess over —reflects not only the particle distribution at any fixed time but also the structure of family trees. The principal property of a historical process is that is a function of for alls<t. Every process with this property is calleda path process. We develop a theory of superprocesses over path processes whose core is the integration with respect to measure-functionals. By applying this theory to historical superprocesses we construct the first hitting distributions and prove a special Markov property for superprocesses.Partially supported by National Science Foundation Grant DMS-8802667     

Primitive recursive estimate of strong normalization for predicate calculus

The strong normalization theorem asserts that any sequence of reductions (standard steps of cut elimination) stops at an object in normal form, i.e., at an object to which further reductions are inapplicable. The most intuitive proofs of strong normalization for various systems, including first- and second-order arithmetic, use, essentially, the concept of hereditary normalizability of an object. This concept, for objects of unbounded complexity, cannot be expressed in the language of arithmetic, so that the proofs mentioned leave its domain. Howard's proof for arithmetic, using nonunique assignment of ordinals, apparently, can be modified so as to get a primitive recursive proof of strict normalizability for the -fragment of the intuitionistic predicate calculus, but the author of the present paper has not succeeded in overcoming the combinatorial difficulties. Our goal is to give an intuitive proof for the predicate calculus, from which one can extract a primitive recursive estimate of the number of reductions, and a proof in primitive recursive arithmetic of the fact that this estimate is proper. The proof of normalizability, that is, the construction of a special reduction sequence stopping at a normal term, is well known. In this sequence one first converts subterms of the highest levell, and first the innermost of them. (Corresponding to this, in the proof one can apply reduction with respect to level.) Here the number of convertible terms of maximal level, suitable for reduction, is lowered and the newly arising convertible terms have lower level.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 131–135, 1979.     

An elementary proof of strong normalization for intersection types

We provide a new and elementary proof of strong normalization for the lambda calculus of intersection types. It uses no strong method, like for instance Tait-Girard reducibility predicates, but just simple induction on type complexity and derivation length and thus it is obviously formalizable within first order arithmetic. To obtain this result, we introduce a new system for intersection types whose rules are directly inspired by the reduction relation. Finally, we show that not only the set of strongly normalizing terms of pure lambda calculus can be characterized in this system, but also that a straightforward modification of its rules allows to characterize the set of weakly normalizing terms. Received: 15 June 1998 / Revised version: 15 November 1999 / Published online: 15 June 2001     

On limit distributions for intermediate order statistics under power normalization

In this paper the work of Chibisov (1964) for the intermediate order statistics, under linear normalization, is extended to the power normalization. The possible limits and the corresponding domains of attraction are derived.     

A strong limit theorem on gambling systems

A strong limit theorem on gambling system for Bernoulli sequences is extended to the sequences of arbitrary discrete random variables by using the conditional probabilities. Furthermore, by allowing the selection function to take values in an interval, the conception of random selection is generalized. In the proof an approach of applying the differentiation of measure on a net to the investigation of the strong limit theorem is proposed.     

Majorizing potentials in strong ratio limit theorems

In this paper, we study the asymptotic properties of the polynomials P _n (z) = P _n (z; f), corresponding to an interpolation table α ? E, where E is a bounded continuum in the complex plane with a connected complement, the table α satisfies the Kakehashi condition, and f is an arbitrary function holomorphic on E. In particular, for zeros of such polynomials, we obtain a generalization of the classical Jentzsch-Szeg? theorem on the distribution of zeros of partial sums of Taylor series.     

Matrix and vector models in the strong coupling limit

We consider matrix and vector models in the large-N limit: we study N × N matrices and vectors with N² components. In the case of a zero-dimensional model (D = 0), we prove that in the strong coupling limit (g → ∞), the partition functions of the two models coincide up to a coefficient. This also holds for D = 1. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 2, pp. 236–243, May, 2008.     

Transformations and non-degenerate maps

We shall prove the equivalences of a non-degenerate circle-preserving map and a Mobius transformation in Rn, of a non-degenerate geodesic-preserving map and an isometry in Hn, of a non-degenerate line-preserving map and an affine transformation in Rn. That a map is non-degenerate means that the image of the whole space under the map is not a circle, or geodesic or line respectively. These results hold without either injective or surjective, or even continuous assumptions, which are new and of a fundamental nature in geometry.     

Transformations and non-degenerate maps

We shall prove the equivalences of a non-degenerate circle-preserving map and a Möbius transformation in\(\hat {\mathbb{R}}^n \), of a non-degenerate geodesic-preserving map and an isometry in ?ⁿ, of a non-degenerate line-preserving map and an affine transformation in ?ⁿ. That a map is non-degenerate means that the image of the whole space under the map is not a circle, or geodesic or line respectively. These results hold without either injective or surjective, or even continuous assumptions, which are new and of a fundamental nature in geometry.     

An exponential inequality and strong limit theorems for conditional expectations

An exponential inequality for the tail of the conditional expectation of sums of centered independent random variables is obtained. This inequality is applied to prove analogues of the Law of the Iterated Logarithm and the Strong Law of Large Numbers for conditional expectations. As corollaries we obtain certain strong theorems for the generalized allocation scheme and for the nonuniformly distributed allocation scheme.     

The strong relaxation limit of the multidimensional Euler equations

This paper is devoted to the analysis of global smooth solutions to the multidimensional isentropic Euler equations with stiff relaxation. We show that the asymptotic behavior of the global smooth solution is governed by the porous media equation as the relaxation time tends to zero. The results are proved by combining some classical energy estimates with the so-called Shizuta–Kawashima condition.     

A general central limit theorem for strong mixing sequences

A central limit theorem for strong mixing sequences is given that applies to both non-stationary sequences and triangular array settings. The result improves on an earlier central limit theorem for this type of dependence given by Politis, Romano and Wolf in 1997.     

U-统计量的一些强极限定理的精确渐近性

设{Xn;n≥1}是一列i.i.d.随机变量序列,Un是以对称函数h(x,y)为核函数的U-统计量.记Un=2n(n-1) 1≤i相似文献