The Annals of Probability

最新文章

• On conservation of probability and the Feller property AI翻译
  作者：Qian, ZM
  摘要：It is known that any smooth, nondegenerate, second-order elliptic operator on a manifold (dimension not equal 2) has the form Delta + B, where B is a vector field and Delta is the Laplace-Beltrami operator under some Riemannian metric on the manifold. In this paper we give several conditions on the ''Ricci curvature'' Ric - del(B)(8) associated with the operator Delta + B to ensure that the diffusion semigroup generated by Delta + B conserves probability and possesses the Feller property.
• Bounding (d)over-bar-distance by informational divergence: A method to prove measure concentration AI翻译
  作者：Marton, K
  摘要：There is a simple inequality by Pinsker between variational distance and informational divergence of probability measures defined on arbitrary probability spaces. We shall consider probability measures on sequences taken from countable alphabets, and derive, from Pinsker's inequality, bounds on the d-distance by informational divergence. Such bounds can be used to prove the ''concentration of measure'' phenomenon for some nonproduct distributions.
• On some boundary crossing problems for Gaussian random walks AI翻译
  作者：Lotov, VI
  摘要：We consider random walks with Gaussian distribution of summands. New representations for Wiener-Kopf factorization components are obtained. The factorization method is used to study the distribution of the excess over one-sided and two-sided boundaries. asymptotic expansions for these distributions and for the expectation of the first exit time are obtained under the assumption that the boundaries tend to infinity.
• Diffusion limits for a nonlinear density dependent space-time population model AI翻译
  作者：Blount, D
  摘要：A population density process is constructed using approximately NI particles performing rate N-2 random walks between N cells distributed on the unit interval. Particles give birth or die within cells, and particle death rates are a function of the occupied cell population. With suitable scaling, two possible limiting stochastic partial differential equations are obtained. Both are nonlinear perturbations of the equation satisfied by the density process of super Brownian motion.
• Singular initial conditions for the heat equation with a noise term AI翻译
  作者：Mueller, C
  摘要：We consider the equation u(t) = u(xx) + u(gamma)W, t > 0, 0 less than or equal to x less than or equal to J, u(0,x) = u(0)(x), u(t,0) = u(t,J) = 0, where W = W(t,x) is two-parameter white noise. We show local existence and uniqueness for unbounded initial conditions satisfying certain conditions. Our results are motivated by earlier work, which showed that, for large gamma, solutions of this equation can blow up. One would wish to show that solutions can be extended beyond blowup, and our resu...
• Hitting probabilities and large deviations AI翻译
  作者：Collamore, JF
  摘要：Let {Y-n}(n is an element of Z+) be a sequence of random variables in R(d) and let A subset of R(d). Then P{Y-n is an element of A for some n} is the hitting probability of the set A by the sequence {Y-n}. We consider the asymptotic behavior, as m --> infinity, of P{Y-n is an element of mA, some n} = P{hitting mA} whenever (1) the probability law of Y-n/n satisfies the large deviation principle and (2) the central tendency of Y-n/n is directed away from the given set A. For a particular functi...
• Enumeration and random random walks on finite groups AI翻译
  作者：Dou, C; Hildebrand, M
  作者单位：University of Texas System; University of Texas Austin
  摘要：This paper examines random walks on a finite group G and finds upper bounds on how long it takes typical random walks supported on (log\G\)(a) elements to get close to uniformly distributed on G. For certain groups, a cutoff phenomenon is shown to exist for these typical random walks. A variation of the upper bound lemma of Diaconis and Shahshahani and some counting arguments related to a group equation are used to get the upper bound. A further example which uses this variation is discussed.
• Nonlinear superprocesses AI翻译
  作者：Overbeck, L
  摘要：Nonlinear martingale problems in the McKean-Vlasov sense for superprocesses are studied. The stochastic calculus on historical trees is used in order to show that there is a unique solution of the nonlinear martingale problems under Lipschitz conditions on the-coefficients.
• On the existence of universal functional solutions to classical SDE's AI翻译
  作者：Kallenberg, O
  摘要：Assume that weak existence and pathwise uniqueness hold for solutions to the equation dX(t) = sigma(t, X) dB(t) + b(t, X) dt starting at fixed points. Then there exists a Borel measurable function F, such that any solution (X, B) satisfies X = F(X(0), B) a.s. This strengthens a fundamental result of Yamada and Watanabe, where F may depend on the initial distribution mu.
• Entropy and the consistent estimation of joint distributions (vol 22, pg 960, 1994) AI翻译
  作者：Marton, K; Shields, PC
  作者单位：University System of Ohio; University of Toledo
  摘要：Jeff Steif has brought to our attention an error on page 975 of our paper. Our argument that inequality (30) implies the immediately following inequality has a gap. A closer look shows an even more serious problem, namely, Lemma 6 as stated is probably not true, since nothing in the weak Bernoulli property precludes the possibility that splitting sets for x(1)(n) may depend on past coordinates {x(1): i less than or equal to 0}. With a modified definition of the splitting concept an alternative...