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作者：Verzani, J
摘要：The planar Brownian snake is a continuous, strong Markov process taking values in the space of continuous functions in R(2) that are stopped at some time. For a fixed time the snake is distributed like a planar Brownian motion with a random lifetime. This paper characterizes the convex hull of the trace of the snake paths that exit the half-plane at the origin. It is shown that the convex hull at 0 is roughly a factor of x smoother than the convex hull of a piece of planar Brownian motion at i...
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作者：Benjamini, I; Schramm, O
摘要：We study a wide class of transient planar graphs, through a geometric model given by a square tiling of a cylinder. For many graphs, the geometric boundary of the tiling is a circle and is easy to describe in general. The simple random walk on the graph converges (with probability 1) to a point in the geometric boundary. We obtain information on the harmonic measure and estimates on the rate of convergence. This allows us to extend results we previously proved for triangulations of a disk.
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作者：Cranston, M; Mountford, TS
作者单位：University of California System; University of California Los Angeles
摘要：We prove the strong law of large numbers for a continuous-time version of reinforced random walk. This extends previous results of Durrett and Rogers.
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作者：Einmahl, U; Mason, DM
作者单位：University of Delaware
摘要：We establish very general one-sided results on the lim sup behavior of increments of suitably normalized partial sums of i.i.d. random variables. Our main results apply to arbitrary nondegenerate positive random variables which need not have any finite moments. As a corollary we can show that such results also hold for not necessarily positive random variables whose negative parts have finite moment-generating functions.
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作者：Toth, B
作者单位：University of Zurich; Heriot Watt University; Centrum Wiskunde & Informatica (CWI)
摘要：We consider non-Markovian, self-interacting random walks (SIRW) on the one-dimensional integer lattice. The walk starts from the origin and at each step jumps to a neighboring site. The probability of jumping along a bond is proportional to w (number of previous jumps along that lattice bond), where w:N --> R(+) is a monotone weight function. Exponential and subexponential weight functions were considered in earlier papers. In the present paper we consider weight functions w with polynomial as...
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作者：Pritchard, G
摘要：The scaled-sample problem asks the following question: given a distribution on a normed linear space E, when do there exist constants {gamma(n)} such that {X((j))/gamma(n)}(n)(j=1) converges as n --> infinity (in the Hausdorff metric given by the norm) to a fixed set K? (Here {X((j))} i.i.d. with the given distribution.) The main result presented here relates the convergence of scaled samples to a large deviation principle for single observations, thereby achieving a dimension-free description...
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作者：Bremaud, P; Massoulie, L
摘要：We address the problem of the convergence to equilibrium of a general class of point processes, containing, in particular, the nonlinear mutually exciting point processes, an extension of the linear Hawkes processes, and give general conditions guaranteeing the existence of a stationary version and the convergence to equilibrium of a nonstationary version, both in distribution and in variation. We also give a new proof of a result of Kerstan concerning point processes with bounded intensity an...
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作者：Bhati, AG; Borkar, VS
作者单位：Indian Institute of Science (IISC) - Bangalore
摘要：For controlled Markov processes taking values in a Polish space, control problems with ergodic cost, infinite-horizon discounted cost and finite-horizon cost are studied. Each is posed as a convex optimization problem wherein one tries to minimize a linear functional on a closed convex set of appropriately defined occupation measures for the problem. These are characterized as solutions of a linear equation asssociated with the problem. This characterization is used to establish the existence ...
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作者：Bunge, J
摘要：A random variable X is N-divisible if it can be decomposed into a random sum of N i.i.d. components, where N is a random variable independent of the components; X is N-stable if the components are rescaled copies of X. These N-divisible and N-stable random variables arise in a variety of stochastic models, including thinned renewal processes and subordinated Levy and stable processes. We consider a general theory of N-divisibility and N-stability in the case where E(N) < infinity, based on a r...
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作者：Bertoin, J; Werner, W
作者单位：Centre National de la Recherche Scientifique (CNRS); University of Cambridge
摘要：We derive the asymptotic laws of winding numbers for planar isotropic stable Levy processes and walks of index alpha is an element of (0, 2).
