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作者：Orsingher, Enzo; Beghin, Luisa
作者单位：Sapienza University Rome
摘要：In this paper the solutions u(nu) = u(nu) (x, t) to fractional diffusion equations of order 0 < v <= 2 are analyzed and interpreted as densities of the composition of various types of stochastic processes. For the fractional equations of order nu = 1/2(n), n >= 1, we show that the solutions u(1/2n) correspond to the distribution of the n-times iterated Brownian motion. For these processes the distributions of the maximum and of the sojourn time are explicitly given. The case of fractional equa...
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作者：Zhao, Ou; Woodroofe, Michael
作者单位：University of Michigan System; University of Michigan
摘要：There has been recent interest in the conditional central limit question for (strictly) stationary, ergodic processes ...., X-1, X-0, X-1 ,... whose partial sums S-n = X-1 + ... + X-n are of the form S-n = M-n + R-n, where M-n is a square integrable martingale with stationary increments and R-n is a remainder term for which E(R-n(2)) = o(n). Here we explore the law of the iterated logarithm (LIL) for the same class of processes. Letting parallel to center dot parallel to denote the norm in L-2...
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作者：Jain, Naresh; Krylov, Nicolai
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Our aim is to unify and extend the large deviation upper and lower bounds for the occupation times of a Markov process with L-2 semigroups under minimal conditions on the state space and the process trajectories for example, no strong Markov property is needed. The methods used here apply in both continuous and discrete time. We present the proofs for Continuous time only because of the inherent technical difficulties in that situation: the proofs can be adapted for discrete time in a straight...
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作者：Fontes, L. R. G.; Mathieu, P.
作者单位：Aix-Marseille Universite
摘要：We study K-processes, which are Markov processes in a denumerable state space, all of whose elements are stable, with the exception of a single state, starting from which the process enters finite sets of stable states with uniform distribution. We show how these processes arise, in a particular instance, as scaling limits of the trap model in the complete graph, and subsequently derive aging results for those models in this context.
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作者：Bertoin, J.; Doney, R. A.; Maller, R. A.
作者单位：Sorbonne Universite; University of Manchester; Australian National University; Australian National University
摘要：We wish to characterize when a Levy process X, crosses boundaries like t(k), K > 0, in a one- or two-sided sense, for small times t; thus, we inquire when lim sup(t down arrow 0) vertical bar X-t vertical bar/t(k), lim sup(t down arrow 0) X-t/t(k) and/or lim inf(t down arrow 0) X-t/t(k) are almost surely (a.s.) finite or infinite. Necessary and sufficient conditions are given for these possibilities for all values Of K > 0. This completes and extends a line of research going back to Blumenthal...
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作者：Bovier, Anton; Faggionato, Alessandra
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technical University of Berlin; Sapienza University Rome
摘要：Sinai's walk can be thought of as a random walk on Z with random potential V, with V weakly converging under diffusive rescaling to a two-sided Brownian motion. We consider here the generator L-N of Sinai's walk on [-N, N] boolean AND Z with Dirichlet conditions on -N, N. By means of potential theory, for each h > 0, we show the relation between the spectral properties of L-N for eigenvalues of order o(exp(-h root N)) and the distribution of the h-extrema of the rescaled potential V-N(x) V(Nx)...
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作者：Nourdin, Ivan
作者单位：Universite Paris Cite; Sorbonne Universite
摘要：The present article is devoted to a fine study of the convergence of renormalized weighted quadratic and cubic variations of a fractional Brownian motion B with Hurst index H. In the quadratic (resp. Cubic) case, when H < 1/4 (resp. H < 1/6). we show by means of Malliavin Calculus that the convergence holds in L(2) toward in explicit limit which only depends on B. This result is somewhat surprising when compared with the celebrated Breuer and Major theorem.
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作者：El Karoui, Mcole; Meziou, Asma
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We are concerned with a new type of supermartingale decomposition in the Max-Plus algebra, which essentially consists in expressing any supermartingale of class (D) as a conditional expectation of some running supremum process. As an application, we show how the Max-Plus supermartingale decomposition allows, in particular, to solve the American optimal stopping problem without having to compute the option price. Some illustrative examples based on one-dimensional diffusion processes are then p...
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作者：Dupuis, Paul; Ishii, Hitoshi
作者单位：Brown University; Waseda University
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作者：Berti, Patrizia; Pratelli, Luca; Rigo, Pietro
作者单位：Universita di Modena e Reggio Emilia; University of Pavia
摘要：Let (Omega, F, P) be a probability space and N the class of those F is an element of F satisfying P(F) is an element of {0, 1}. For each G subset of F, define (G) over bar = sigma(G boolean OR N). Necessary and sufficient conditions for (A) over bar boolean AND (B) over bar = (A boolean AND B) over bar, where A, B subset of F are sub-sigma-fields, are given. These conditions are then applied to the (two-component) Gibbs sampler. Suppose X and Y are the coordinate projections on (Omega, F) = (X...
