Mathematics and Statistics
Mathematics plays a critical role in efforts to understand the nature of the physical universe and in the continuing development of technology. Emphasizing excellence in both research and teaching, the Mathematics & Statistics Department at BU offers a wide range of courses in pure and applied mathematics and statistics at the undergraduate and graduate level. The department has particularly strong groups in dynamical systems and applications, geometry/topology, mathematical physics, number theory, and probability and statistics.
Department chair: Tasso Kaper
Campus address: 111 Cummington Street
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(Freiburger Zentrum für Dateanlyse und Modellbildung, Albert-Ludwigs-Universität, Freiburg im Breslau, Germany ( Freiburg Center for Data Analysis and Modeling, Albert-Ludwigs-Universität, Freiburg im Wroclaw, Germany), 1995-03)ARCH-models have become popular for modelling financial time series. The seem, at first, however, to be incompatible with the option pricing approach of Black, Scholes, Merton et al., because they are discrete-time models ...
(1984-01)A process X(t) is self-similar with index H > 0 if the finite-dimensional distributions of X(at) are identical to those of aHX(t) for all a > 0. Consider self-similar processes X(t) that are Gaussian or that can be represented ...
(1994-10)We study Slepian inequalities for general non-Gaussian infinitely divisible random vectors. Conditions for such inequalities are expressed in terms of the corresponding Levy measures of these vectors. These conditions are ...
(Institute of Mathematical Statistics, 1991-11)Let (X1,X2) be an α-stable random vector, not necessarily symmetric, with 0<α<2. This article investigates the regression E(X2∣X1=x) for all values of α. We give conditions for the existence of the conditional moment ...
(1995-09)A class of α-stable, 0\textlessα\textless2, processes is obtained as a sum of ’up-and-down’ pulses determined by an appropriate Poisson random measure. Processes are H-self-affine (also frequently called ’self-similar’) ...
(ELSEVIER INC, 1991-04-01)This paper studies the sample path properties of stochastic processes represented by multiple symmetric α-stable integrals. It relates the “smoothness” of the sample paths to the “smoothness” of the (non-random) integrand. ...
(INST MATHEMATICAL STATISTICS, 1992-01-01)Skorohod has shown that the convergence of sums of i.i.d. random variables to an a-stable Levy motion, with 0 < a < 2, holds in the weak-J1 sense. J1 is the commonly used Skorohod topology. We show that for sums of moving ...
(Institute of Mathematical Statistics, 1989-12-01)Let (Xj)∞ j = 1 be a stationary, mean-zero Gaussian process with covariances r(k) = EXk + 1 X1 satisfying r(0) = 1 and r(k) = k-DL(k) where D is small and L is slowly varying at infinity. Consider the two-parameter empirical ...
(ELSEVIER SCIENCE BV, 1989-10-01)Billingsley developed a widely used method for proving weak convergence with respect to the sup-norm and J -Skorohod topologies, once convergence of the finite-dimensional distributions has been established. Billingsley's ...