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作者：de Acosta, A
作者单位：University System of Ohio; Case Western Reserve University
摘要：We obtain lower bounds for moderate deviations of empirical measures of a Markov chain with general state space under the assumption of ergodicity of degree 2. We derive an explicit expression for the rate function.
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作者：Bobkov, S
摘要：The isoperimetric problem for log-concave product measures in R(n) equipped with the uniform distance is considered. Necessary and sufficient conditions under which standard half-spaces are extremal are presented.
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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：Bercovici, H; Pata, V
摘要：Let X(1),X(2),... be a sequence of free identically distributed random variables, with common distribution mu. It was shown by Lindsay and Pata, in a more general context, that a sufficient condition for the weak law of large numbers to hold for the sequence X(1), X(2),... is that (t-->infinity)lim t mu({x: \x\ > t}) = 0. We show that this condition is necessary as well as sufficient. Even though the condition is identical with the corresponding one for commuting independent variables, the pro...
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作者：Newman, CM; Volchan, SB
摘要：Consider an inhomogeneous contact process on Z(1) in which the recovery rates delta(x) at site I: are i.i.d. random variables (bounded above) while the infection rate is a constant epsilon. The condition uP(-log delta(x) > u) --> + infinity as u --> + infinity. implies the survival of the process for every epsilon > 0.
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作者：Vitale, RA
摘要：The Wills functional from the theory of lattice point enumeration can be adapted to produce the following exponential inequality for zero-mean Gaussian processes: E exp[sup(t)(X(t) - (1/2)sigma(t)(2))] less than or equal to exp(E sup(t)X(t)). An application is a new proof of the deviation inequality for the supremum of a Gaussian process above its mean: P(sup(t)X(t) - E sup(t)X(t) greater than or equal to a) less than or equal to exp(-(1/2)alpha(2)/sigma(2)), where alpha > 0 and sigma(2) = sup...
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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：Feldman, J; Tsirelson, B
作者单位：Tel Aviv University
摘要：Sharpening the main result of the preceding paper, it is shown that if B-t, 0 less than or equal to t < infinity, is a standard Brownian motion on (Omega,f,P), then for any epsilon > 0 there is a probability measure Q with (1 - epsilon)P less than or equal to Q less than or equal to (1 + epsilon)P such that the filtration of B cannot be generated by any Brownian motion on (Omega,F,Q).
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作者：Cvitanic, J; Karatzas, I
作者单位：Columbia University
摘要：We establish existence and uniqueness results for adapted solutions of backward stochastic differential equations (BSDE's) with two reflecting barriers, generalizing the work of El Karoui, Kapoudjian, Pardoux, Peng and Quenez. Existence is proved first by solving a related pair of coupled optimal stopping problems, and then, under different conditions, via a penalization method. It is also shown that the solution coincides with the value of a certain Dynkin game, a stochastic game of optimal s...
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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.
