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作者：Da Costa, Conrado; Menshikov, Mikhail, V; Wade, Andrew r.
作者单位：Durham University
摘要：We study recurrence and transience for a particle that moves at constant velocity in the interior of an unbounded planar domain, with random reflections at the boundary governed by a Markov kernel producing outgoing angles from incoming angles. Our domains have a single unbounded direction and sub-linear growth. We characterize recurrence in terms of the reflection kernel and growth rate of the domain. The results are obtained by transform-ing the stochastic billiards model to a Markov chain o...
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作者：He, Jimmy; Ottolini, Andrea
作者单位：Massachusetts Institute of Technology (MIT); University of Washington; University of Washington Seattle
摘要：Consider a uniformly random deck consisting of cards labelled by num-bers from 1 through n , possibly with repeats. A guesser guesses the top card, after which it is revealed and removed and the game continues. What is the expected number of correct guesses under the best and worst strategies? We establish sharp asymptotics for both strategies. For the worst case, this an-swers a recent question of Diaconis, Graham, He and Spiro, who found the correct order. As part of the proof, we study the ...
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作者：Liu, Yating; Pages, Gilles
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：We establish the functional convex order results for two scaled McKean- Vlasov processes X = (X-t)(t is an element of[0 ,T] )and Y = (Y-t)(t is an element of[0 ,T]) defined on a filtered probability space (Omega,F,(F-t)(t >= 0) , P) by{dX(t )= b(t, X-t , mu(t))d(t) + sigma (t, X-t , mu(t))dB(t) , X-0 is an element of L-p(P),dY(t) = b(t,Y-t ,nu(t))d(t) + theta(t, Y-t , nu(t))dB(t) , Y-0 is an element of L-p(P), where p >= 2, for every t is an element of [0 , T ] , mu(t) , nu t denote the probab...
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作者：Vechambre, Gregoire
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：Wright-Fisher diffusions describe the evolution of the type composition of an infinite haploid population with two types (say type 0 and type 1) subject to neutral reproductions, and possibly selection and mutations. In the present paper we study a Wright-Fisher diffusion in a Levy environment that gives a selective advantage to sometimes one type, sometimes the other. Classical methods using the ancestral selection graph (ASG) fail in the study of this model because of the complexity, resulti...
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作者：Banerjee, Sayan; Brown, Brendan
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We describe and analyze a class of positive recurrent reflected Brownian motions (RBMs) in Rd+ for which local statistics converge to equilibrium at a rate independent of the dimension d. Under suitable assumptions on the reflection matrix, drift and diffusivity coefficients, dimension-independent stretched exponential convergence rates are obtained by estimating contrac-tions in an underlying weighted distance between synchronously coupled RBMs. We also study the symmetric Atlas model as a fi...
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作者：Foo, Jasmine; Gunnarsson, Einar Bjarki; Leder, Kevin; Storey, Kathleen
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Minnesota System; University of Minnesota Twin Cities; Lafayette College
摘要：Over 80% of human cancers originate from the epithelium, which covers the outer and inner surfaces of organs and blood vessels. In stratified epithe-lium, the bottom layers are occupied by stem and stem-like cells that contin-ually divide and replenish the upper layers. In this work, we study the spread of premalignant mutant clones and cancer initiation in stratified epithelium, using the biased voter model on stacked two-dimensional lattices. Our main result is an estimate of the propagation...
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作者：Lehmann, Tobias
作者单位：Leipzig University
摘要：We prove that stochastic replicator dynamics can be interpreted as intrin-sic Brownian motion on the simplex equipped with the Aitchison geometry. As an immediate consequence, we derive three approximation results in the spirit of Wong-Zakai approximation, Donsker's invariance principle and a JKO-scheme. Using the Fokker-Planck equation and Wasserstein-contraction estimates, we also study the long time behavior of the stochastic replicator equation, as an example of a nongradient drift diffusi...
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作者：Ararat, Cagin; Ma, Jin; Wu, Wenqian
作者单位：Ihsan Dogramaci Bilkent University; University of Southern California
摘要：In this paper, we establish an analytic framework for studying set -valued backward stochastic differential equations (set-valued BSDE), motivated largely by the current studies of dynamic set-valued risk measures for multi-asset or network-based financial models. Our framework will make use of the notion of the Hukuhara difference between sets, in order to compensate the lack of inverse operation of the traditional Minkowski addition, whence the vector space structure in set-valued analysis. ...
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作者：Hirsch, Christian; Owada, Takashi
作者单位：Aarhus University; Purdue University System; Purdue University
摘要：We prove a large deviation principle for the point process associated to k-element connected components in R-d with respect to the connectivity radii r(n)->infinity. The random points are generated from a homogeneous Poisson point process or the corresponding binomial point process, so that (r(n))(n >= 1) satisfies n(k)r(n)(d(k-1))n ->infinity and nr(n)(d) -> 0 as n -> infinity (i.e., sparse regime). The rate function for the obtained large deviation principle can be represented as relative en...
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作者：Hilario, Marcelo R.; Sa, Marcos; Sanchis, Remy; Teixeira, Augusto
作者单位：Universidade Federal de Minas Gerais; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：Let {& xi;i}i & GE;1 be a sequence of i.i.d. positive random variables. Starting from the usual square lattice replace each horizontal edge that links a site in the ith vertical column to another in the (i + 1)th vertical column by an edge having length & xi;i. Then declare independently each edge e in the resulting lattice open with probability pe = p|e| where p & ISIN; [0, 1] and |e| is the length of e. We relate the occurrence of a nontrivial phase transition for this model to moment proper...
