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作者：Di Tella, Paolo; Engelbert, Hans-Juergen
作者单位：Technische Universitat Dresden; Friedrich Schiller University of Jena
摘要：In the present paper, we study the chaotic representation property for certain families X of square integrable martingales on a finite time interval [0, T]. For this purpose, we introduce the notion of compensated-covariation stability of such families. The chaotic representation property will be defined using iterated integrals with respect to a given family of square integrable martingales having deterministic mutual predictable covariation < X, Y > for all X, Y is an element of X. The main ...
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作者：Hu, Yueyun; Shi, Zhan
作者单位：Universite Paris 13
摘要：We are interested in the randomly biased random walk on the supercritical Galton-Watson tree. Our attention is focused on a slow regime when the biased random walk (X-n) is null recurrent, making a maximal displacement of order of magnitude (log n)(3) in the first n steps. We study the localization problem of X-n and prove that the quenched law of X-n can be approximated by a certain invariant probability depending on n and the random environment. As a consequence, we establish that upon the s...
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作者：Saloff-Coste, Laurent; Zheng, Tianyi
作者单位：Cornell University; Stanford University
摘要：Let G be a finitely generated group equipped with a finite symmetric generating set and the associated word length function vertical bar center dot vertical bar. We study the behavior of the probability of return for random walks driven by symmetric measures cc that are such that Sigma rho (vertical bar x vertical bar mu(x) < infinity for increasing regularly varying or slowly varying functions rho, for instance, s vertical bar -> (1 + s)(alpha), alpha is an element of(0, 2], or s vertical bar...
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作者：Chevyrev, Ilya; Lyons, Terry
作者单位：University of Oxford; University of Oxford
摘要：We define a characteristic function for probability measures on the signatures of geometric rough paths. We determine sufficient conditions under which a random variable is uniquely determined by its expected signature, thus partially solving the analogue of the moment problem. We furthermore study analyticity properties of the characteristic function and prove a method of moments for weak convergence of random variables. We apply our results to signature arising from Levy, Gaussian and Markov...
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作者：Mukherjee, Chiranjib; Varadhan, S. R. S.
摘要：In proving large deviation estimates, the lower bound for open sets and upper bound for compact sets are essentially local estimates. On the other hand, the upper bound for closed sets is global and compactness of space or an exponential tightness estimate is needed to establish it. In dealing with the occupation measure L-t(A) = 1/t integral(t)(0) 1(A)(W-s) ds of the d-dimensional Brownian motion, which is not positive recurrent, there is no possibility of exponential tightness. The space of ...
