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作者：Chen, Zhen-Qing; Zhang, Tusheng
作者单位：University of Washington; University of Washington Seattle; University of Manchester
摘要：In this paper, we prove that there exists a unique, bounded continuous weak solution to the Dirichlet boundary value problem for a general class of second-order elliptic operators with singular coefficients, which does not necessarily have the maximum principle. Our method is probabilistic. The time reversal of symmetric Markov processes and the theory of Dirichlet forms play a crucial role in our approach.
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作者：Peng, Shige; Yang, Zhe
作者单位：Shandong University
摘要：In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also the future. We show that these anticipated BSDEs have unique solutions, a comparison theorem for their solutions, and a duality between them and stochastic differential delay equations.
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作者：Caravenna, Francesco; Deuschel, Jean-Dominique
作者单位：University of Padua; Technical University of Berlin
摘要：We consider a random field phi: {1,..., N} -> R with Laplacian interaction of the form Sigma(i) V(Delta phi(i)), where Delta is the discrete Laplacian and the potential V(.) is symmetric and uniformly strictly convex. The pinning model is defined by giving the field a reward epsilon >= 0 each time it touches the x-axis, OF that plays the role of a defect line. It is known that this model exhibits a phase transition between a delocalized regime (epsilon < epsilon(c)) and a localized one (epsilo...
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作者：Lember, Jueri; Matzinger, Heinrich
作者单位：University of Tartu; University System of Georgia; Georgia Institute of Technology
摘要：Let L-n be the length of the longest common subsequence of two independent i.i.d. sequences of Bernoulli variables of length n, We prove that the order of the standard deviation of L-n is root n, provided the parameter of the Bernoulli variables is small enough. This validates Waterman's conjecture in this situation [Philos. Trans. R. Soc. Lond. Ser B 344 (1994) 383-390]. The order conjectured by Chvatal and Sankoff [J. Appl. Probab. 12 (1975) 306-315], however, is different.
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作者：Erdos, Laszlo; Schlein, Benjamin; Yau, Horng-Tzer
作者单位：University of Munich; Harvard University
摘要：We consider N x N Hermitian random matrices with i.i.d. entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order 1/N. We study the connection between eigenvalue statistics on microscopic energy scales eta << 1 and (de)localization properties of the eigenvectors. Under suitable assumptions on the distribution of the single matrix elements, we first give an upper bound on the density of states on short energy scales of order eta similar to log N/N...
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作者：Meerschaert, Mark M.; Nane, Erkan; Vellaisamy, P.
作者单位：Michigan State University; Auburn University System; Auburn University; Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Bombay
摘要：Fractional Cauchy problems replace the usual first-order time derivative by a fractional derivative. This paper develops classical solutions and stochastic analogues for fractional Cauchy problems in a bounded domain D subset of R-d with Dirichlet boundary conditions. Stochastic solutions are constructed via an inverse stable subordinator whose scaling index corresponds to the order of the fractional time derivative. Dirichlet problems corresponding to iterated Brownian motion in a bounded dom...
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作者：Cox, J. Theodore; Schinazi, Rinaldo B.
作者单位：Syracuse University; University of Colorado System; University of Colorado at Colorado Springs
摘要：We study the ergodic theory of a multitype contact process with equal death rates and unequal birth rates on the d-dimensional integer lattice and OF regular trees. We prove that for birth rates in a certain interval there is coexistence on the tree, which by a result of Neuhauser is not possible on the lattice. We also prove a complete convergence result when the larger birth rate falls outside of this interval.
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作者：von Renesse, Max-K.; Sturm, Karl-Theodor
作者单位：Technical University of Berlin; University of Bonn
摘要：We construct a new random probability measure on the circle and on the unit interval which in both cases has a Gibbs structure with the relative entropy functional as Hamiltonian. It satisfies a quasi-invariance formula with respect to the action of smooth diffeomorphism of the sphere and the interval, respectively. The associated integration by parts formula is used to construct two classes of diffusion processes on probability measures (on the sphere or the unit interval) by Dirichlet form m...
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作者：Croydon, David A.
作者单位：University of Warwick
摘要：A Brownian spatial tree is defined to be a pair (T, phi), where T is the rooted real tree naturally associated with a Brownian excursion and phi is a random continuous function from T into R(d) such that, conditional on T, phi maps each arc of T to the image of a Brownian motion path in R(d) run for a time equal to the arc length. It is shown that, in high dimensions, the Hausdorff measure of arcs can be used to define an intrinsic metric d(s) on the set S := phi(T). Applications of this resul...
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作者：Addario-Berry, Louigi; Reed, Bruce
作者单位：Universite de Montreal; McGill University; Inria; Universite Cote d'Azur
摘要：Given a branching random walk, let M-n be the minimum position of any member of the nth generation. We calculate EMn to within O(1) and prove exponential tail bounds for P{vertical bar M-n - EMn vertical bar > x}, under quite general conditions on the branching random walk. In particular, together with work by Bramson [Z. Wahrsch. Verw. Gebiete 45 (1978) 89-108], our results fully characterize the possible behavior of EMn when the branching random walk has bounded branching and step size.
