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PHYSICAL REVIEW LETTERS, ISSN 0031-9007, 07/2019, Volume 123, Issue 2, p. 020201
We revisit a family of integrals that delude intuition and that recently appeared in mathematical literature in connection with computer algebra package verification... 
PHYSICS, MULTIDISCIPLINARY | SINC | Random walk theory | Program verification (computers) | Integrals | Computer algebra | Random walk | Physics
Journal Article
Reports on progress in physics, ISSN 1361-6633, 2017, Volume 80, Issue 4, p. 046601
Journal Article
ELECTRONIC JOURNAL OF PROBABILITY, ISSN 1083-6489, 2019, Volume 24
Journal Article
Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, ISSN 1350-7265, 2019, Volume 25, Issue 3, pp. 1755 - 1769
.... In this paper, we establish a growth condition in terms of q and f such that the perpetual integral integral(infinity)(0) integral(X... 
Feller process | Levy process | perpetual integral | STATISTICS & PROBABILITY | conservativeness | random time change | FUNCTIONALS
Journal Article
Annals of physics, ISSN 0003-4916, 2016, Volume 368, pp. 191 - 247
Journal Article
Pattern recognition, ISSN 0031-3203, 2013, Volume 46, Issue 11, pp. 3056 - 3065
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 6/2014, Volume 196, Issue 3, pp. 589 - 650
We prove that a set of density one satisfies the local-global conjecture for integral Apollonian gaskets... 
Mathematics, general | Mathematics | MATHEMATICS | CIRCLE PACKINGS | GENERATION | RANDOM-WALKS | EXPANSION | GEOMETRY | Integers | Obstructions | Integrals | Mathematical analysis | Gaskets | Density | Curvature
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 9/2016, Volume 29, Issue 3, pp. 717 - 736
Weak convergence of various general functionals of partial sums of dependent random variables to stochastic integrals now plays a major role in modern statistics theory... 
Weak convergence | Causal process | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | 60H05 | 60F17 | Stochastic integral | REGRESSION | ITERATED RANDOM FUNCTIONS | UNIT-ROOT | STATISTICS & PROBABILITY | LINEAR-PROCESSES | ASYMPTOTICS | CENTRAL-LIMIT-THEOREM | Stochastic processes
Journal Article
Journal Article
Quarterly of Applied Mathematics, ISSN 0033-569X, 2018, Volume 76, Issue 3, pp. 577 - 600
.... We evaluate these sums with multiple integration, a modern technique. First, we start with three different double integrals that have been previously used in the literature to show zeta(2) = pi(2... 
Polytope | Multiple integrals | Random variables | Basel Problem | ZETA | MATHEMATICS, APPLIED | random variables | PROOF | multiple integrals | polytope | Mathematics - Probability
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 6/2019, Volume 32, Issue 2, pp. 1051 - 1075
We consider the spherical integral of real symmetric or Hermitian matrices when the rank of one matrix is one... 
15B52 | Random matrices | Free probability | Asymptotic expansion | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Spherical integral | 46L54 | STATISTICS & PROBABILITY
Journal Article
Expositiones mathematicae, ISSN 0723-0869, 2011, Volume 29, Issue 1, pp. 67 - 109
We present the Walsh theory of stochastic integrals with respect to martingale measures, and various extensions of this theory, alongside of the Da Prato and Zabczyk theory of stochastic integrals... 
Random field solution | Cylindrical Wiener process | Stochastic wave equation | Stochastic heat equation | Stochastic partial differential equation | Spatially homogeneous Gaussian noise | Hilbert-space-valued Wiener process | Stochastic integral | Martingale measure | EXISTENCE | LAW | SMOOTHNESS | CAUCHY-PROBLEM | NOISE | SPACE | MATHEMATICS | DIMENSIONS | WIENER PROCESS | WAVE-EQUATION
Journal Article