The Annals of Probability

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• THE CONTOUR OF SPLITTING TREES IS A LEVY PROCESS AI翻译
  作者：Lambert, Amaury
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; Sorbonne Universite
  摘要：Splitting trees are those random trees where individuals give birth at a constant rate during a lifetime with general distribution, to i.i.d. copies of themselves. The width process of a splitting tree is then a binary, homogeneous Crump-Mode-Jagers (CMJ) process, and is not Markovian unless the lifetime distribution is exponential (or a Dirac mass at {infinity}). Here, we allow the birth rate to be infinite, that is, pairs of birth times and life spans of newborns form a Poisson point process...
• q-EXCHANGEABILITY VIA QUASI-INVARIANCE AI翻译
  作者：Gnedin, Alexander; Olshanskii, Grigori
  作者单位：Utrecht University; Kharkevich Institute for Information Transmission Problems of the RAS
  摘要：For positive q not equal 1, the q-exchangeability of an infinite random word is introduced as quasi-invariance under permutations of letters, with a special cocycle which accounts for inversions in the word. This framework allows us to extend the q-analog of de Finetti's theorem for binary sequences-see Gresehonig and Schmidt [Colloq. Math. 84/85 (2000) 495-514]-to general real-valued sequences. In contrast to the classical case of exchangeability (q = 1), the order on R plays a significant ro...
• HOMOGENEOUS NUCLEATION FOR GLAUBER AND KAWASAKI DYNAMICS IN LARGE VOLUMES AT LOW TEMPERATURES AI翻译
  作者：Bovier, Anton; den Hollander, Frank; Spitoni, Cristian
  作者单位：University of Bonn; Leiden University; Leiden University - Excl LUMC
  摘要：In this paper, we study metastability in large volumes at low temperatures. We consider both Ising spins subject to Glauber spin-flip dynamics and lattice gas particles subject to Kawasaki hopping dynamics. Let beta denote the inverse temperature and let Lambda(beta) subset of Z(2) be a square box with periodic boundary conditions such that lim(beta ->infinity) vertical bar Lambda(beta)vertical bar = infinity. We run the dynamics on Lambda(beta), starting from a random initial configuration wh...
• TAYLOR EXPANSIONS OF SOLUTIONS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH ADDITIVE NOISE AI翻译
  作者：Jentzen, Arnulf; Kloeden, Peter
  作者单位：Goethe University Frankfurt
  摘要：The solution of a parabolic stochastic partial differential equation (SPDE) driven by an infinite-dimensional Brownian motion is in general not a semi-martingale anymore and does in general not satisfy an Ito formula like the solution of a finite-dimensional stochastic ordinary differential equation (SODE). In particular, it is not possible to derive stochastic Taylor expansions as for the solution of a SODE using an iterated application of the Ito formula. Consequently, until recently, only l...
• SEMI-CLASSICAL ANALYSIS OF A RANDOM WALK ON A MANIFOLD AI翻译
  作者：Lebeau, Gilles; Michel, Laurent
  作者单位：Universite Cote d'Azur
  摘要：We prove a sharp rate of convergence to stationarity for a natural random walk on a compact Riemannian manifold (M, g). The proof includes a detailed study of the spectral theory of the associated operator.
• OPTIMAL LOCAL HOLDER INDEX FOR DENSITY STATES OF SUPERPROCESSES WITH (1+β)-BRANCHING MECHANISM AI翻译
  作者：Fleischmann, Klaus; Mytnik, Leonid; Wachtel, Vitali
  作者单位：Technion Israel Institute of Technology; University of Munich
  摘要：For 0 < alpha <= 2, a super-alpha-stable motion X in R(d) with branching of index 1 + beta is an element of (1,2) is considered. Fix arbitrary t > 0. If d < alpha/beta, a dichotomy for the density function of the measure X(t) holds: the density function is locally Holder continuous if d = 1 and alpha > 1 + beta but locally unbounded otherwise. Moreover, in the case of continuity, we determine the optimal local Holder index.
• A STOCHASTIC DIFFERENTIAL GAME FOR THE INHOMOGENEOUS ∞-LAPLACE EQUATION AI翻译
  作者：Atar, Rami; Budhiraja, Amarjit
  作者单位：Technion Israel Institute of Technology; University of North Carolina; University of North Carolina Chapel Hill
  摘要：Given a bounded C(2) domain G subset of R(m), functions g is an element of C(partial derivative G, R) and h is an element of C((G) over bar, R backslash {0}), let u denote the unique viscosity solution to the equation -2 Delta(infinity)u = h in G with boundary data g. We provide a representation for u as the value of a two-player zero-sum stochastic differential game.
• RANDOM WALKS ON DISCRETE CYLINDERS WITH LARGE BASES AND RANDOM INTERLACEMENTS AI翻译
  作者：Windisch, David
  作者单位：Weizmann Institute of Science
  摘要：Following the recent work of Sznitman [Probab. Theory Related Fields 145 (2009) 143-174], we investigate the microscopic picture induced by a random walk trajectory on a cylinder of the form G(N) x Z, where G(N) is a large finite connected weighted graph, and relate it to the model of random interlacements on infinite transient weighted graphs. Under suitable assumptions, the set of points not visited by the random walk until a time of order vertical bar G(N)vertical bar(2) in a neighborhood o...
• HEAT KERNEL ESTIMATES FOR THE FRACTIONAL LAPLACIAN WITH DIRICHLET CONDITIONS AI翻译
  作者：Bogdan, Krzysztof; Grzywny, Tomasz; Ryznar, Michal
  作者单位：Wroclaw University of Science & Technology
  摘要：We give sharp estimates for the heat kernel of the fractional Laplacian with Dirichlet condition for a general class of domains including Lipschitz domains.
• RIGHT INVERSES OF LEVY PROCESSES AI翻译
  作者：Doney, Ron; Savov, Mladen
  作者单位：University of Manchester; University of Oxford
  摘要：We call a right-continuous increasing process K-lambda a partial right inverse (PRI) of a given Levy process X if X-K lambda = x for at least all x in some random Interval vertical bar 0. zeta) of positive length In this paper. we give a necessary and sufficient condition for the existence of a PRI in terms of the Levy triplet