Mathematics Scholarly Works: Recent submissions
Now showing items 221-240 of 283
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Ordered Spaces all of whose Continuous Images are Normal
(American Mathematical Society, 1989-01-01)Some spaces, such as compact Hausdorff spaces, have the property that every regular continuous image is normal. In this paper, we look at such spaces. In particular, it is shown that if a normal space has finite ... -
On Q-sets
(American Mathematical Society, 1980-02-01)A Q set is an uncountable set X of the real line such that every subset of X is an F„ relative to X. It is known that die existence of a Q set is independent of and consistent with the usual axioms of set theory. We show ... -
Normal Moore Spaces in the Constructible Universe
(American Mathematical Society, 1974-11-01)Assuming the axiom of constructibility, points in closed discrete subspaces of certain normal spaces can be simultaneously separated.This is a partial result towards the normal Moore space conjecture. -
Martin's Axiom Implies that de Caux's Space is Countably Metacompact
(American Mathematical Society, 1980-11-01)De Caux defined a space 5(E) and, assuming *, showed that S(t) is normal but not countably metacompact. We assume MA„ and show that 5(E) is countably metacompact. -
Lemma on Measurable Cardinals
(American Mathematical Society, 1975-06-01)An ordinal is moved by only finitely many measurable cardinals. -
Discrete Sets of Singular Cardinality
(American Mathematical Society, 1983-08-02)Let « be a singular cardinal. In Fleissner's thesis, he showed that in normal spaces X, certain discrete sets Y of cardinality a (called here sparse) which are < ic-separated are, in fact, separated. In Watson's thesis, ... -
Cofinality in normal, almost compact spaces
(American Mathematical Society, 1991-10-01)A regular space is said to be a NAC space if, given any pair of disjoint closed subsets, one of them is compact. The standard example of a noncompact NAC space is an ordinal space of uncountable cofinality. The coñnality ... -
Normal Subspaces of Products of Ordinals
(American Mathematical Society, 2002-12-01)Let X be a subspace of the product of nitely many ordinals. If X is normal, then X is strongly zero-dimensional, collectionwise normal, and shrinking. The proof uses ( 1; : : : ; n)-stationary sets. -
Metacompact Subspaces of Products or Ordinals
(American Mathematical Society, 2001-05-01)Let X be a subspace of the product of nitely many ordinals. X is countably metacompact, and X is metacompact i X has no closed subset homeomorphic to a stationary subset of a regular uncountable cardinal. A theorem ... -
Son of George and V = L
(Association for Symbolic Logic, 1983-03-01)This paper has three parts. In this first part, we formulate and prove from V = L a new combinatorial principle, ⋄++. In the second part, we discuss the topological problem which led to the formulation of ⋄++. Finally, we ... -
NORMALITY VERSUS COUNTABLE PARACOMPACTNESS IN PERFECT SPACES
(American Mathematical Society, 1976-07-01) -
Normal, Not Paracompact Spaces
(American Mathematical Society, 1982-07-01)We describe some recently constructed counterexamples in general topology, including a normal, nonmetrizable Moore space, a normal para-Lindelof, not paracompact space, and a normal, screenable, not paracompact space. -
Large deviation for diffusions and Hamilton-Jacobi equation in Hilbert spaces
(Institute of Mathematical Statistics, 2006-01-01)Large deviation for Markov processes can be studied by Hamilton– Jacobi equation techniques. The method of proof involves three steps: First, we apply a nonlinear transform to generators of the Markov processes, and verify ... -
Short-maturity asymptotics for a fast mean reverting stochastic volatility model
(Society for Industrial and Applied Mathematics, 2010-02-10)In this paper, we study the Heston stochastic volatility model in a regime where the maturity is small but large compared to the mean-reversion time of the stochastic volatility factor. We derive a large deviation principle ... -
SMALL-TIME ASYMPTOTICS FOR FAST MEAN-REVERTING STOCHASTIC VOLATILITY MODELS
(Institute of Mathematical Statistics, 2012-01-01)In this paper, we study stochastic volatility models in regimes where the maturity is small, but large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the class of averaging/ ... -
Semilinear stochastic equations in a Hilbert space with a fractional Brownian motion
(Society for Industrial and Applied Mathematics, 2009-02-01)The solutions of a family of semilinear stochastic equations in a Hilbert space with a fractional Brownian motion are investigated. The nonlinear term in these equations has primarily only a growth condition assumption. ... -
Linear-quadratic fractional Gaussian control
(Society for Industrial and Applied Mathematics, 2013-01-01)In this paper a control problem for a linear stochastic system driven by a noise process that is an arbitrary zero mean, square integrable stochastic process with continuous sample paths and a cost functional that is ... -
On the solutions of a stochastic control system II
(Society for Industrial and Applied Mathematics, 1975-01-01)This paper presents generalizations of the work in [1], [2] to include controlled stochastic processes which take values in a certain class of Frechet spaces. The crucial result is an extension of Girsanov’s technique for ... -
On the solutions of a stochastic control system
(Society for Industrial and Applied Mathematics, 1971-01-01)The control system considered in this paper is modeled by the stochastic differential equation dx(t, to) f(t, x(., o), u(t, to)) dt + dB(t, to), where B is n-dimensional Brownian motion, and the control u is a nonanticipative ... -
Stochastic control problems and spherical functions on symmetric spaces
(American Mathematical Society, 1995-01-01)A family of explicitly solvable stochastic control problems is formulated and solved in noncompact symmetric spaces. The symmetric spaces include all of the classical spaces and four of the exceptional spaces. The ...
