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作者：SOWERS, RB
摘要：In this paper we establish a large deviations principle for the non-Gaussian stochastic reaction-diffusion equation (SRDE) partial derivative(t)upsilon(epsilon) = L(upsilon)epsilon + f(x, upsilon(epsilon)) + epsilon-sigma(x, upsilon(epsilon))W(tx) as a random perturbation of the deterministic RDE partial derivative(t)upsilon-0 = L-upsilon-0 + f(x, upsilon-0). Here the space variable takes values on the unit circle S1 and L is a strongly-elliptic second-order operator with constant coefficients...
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作者：CHEN, HN
摘要：In this paper we study a growth model known as the contact process with sexual reproduction on Z2. We focus on the symmetric model in which a child particle can be produced at a vacant site whenever a pair of its neighboring sites is occupied by parent particles. Two kinds of stability of the absorbing state-phi (i,e., the state in which all the sites are vacant) are investigated in this paper. The first kind of stability concerns the behavior of the system when it starts close to the state-ph...
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作者：FITZSIMMONS, PJ; KANDA, M
作者单位：University of Tsukuba
摘要：Following Choquet, the capacity associated with a Markov process is said to be dichotomous if each compact set K contains two disjoint sets with the same capacity as K. In the context of right processes, we prove that the dichotomy of capacity is equivalent to Hunt's hypothesis that semipolar sets are polar. We also show that a weaker form of the dichotomy is valid for any Levy process with absolutely continuous potential kernel.
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作者：HAHN, MG; WEINER, DC
作者单位：Boston University
摘要：Let {X(j)} be independent, identically distributed random variables with continuous nondegenerate distribution F which is symmetric about the origin. Let {X(n)(1), X(n)(2), . . . , X(n)(n)} denote the arrangement of {X1, . . ., X(n)} in decreasing order of magnitude, so that with probability 1, \X(n)(1)\ > \X(n)(2)\ > ... > \X(n)(n)\. For integers r(n) --> infinity such that r(n)/n --> 0, define the self-normalized trimmed sum T(n) = SIGMA(i = r(n))nX(n)(i)/{SIGMA(i = r(n))nX(n)2(i)}1/2. The a...
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作者：TALAGRAND, M
作者单位：Sorbonne Universite
摘要：For very general random Fourier series and infinitely divisible processes on a locally compact Abelian group G, a necessary and sufficient condition for sample continuity is given in terms of the convergence of a certain series. This series expresses a control on the covering numbers of a compact neighborhood of G by certain nonrandom sets naturally associated with the Fourier series (resp. the process). In the nonstationary case, we give a necessary Sudakov-type condition for a probability me...
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作者：BRYDGES, D; EVANS, SN; IMBRIE, JZ
作者单位：University of California System; University of California Berkeley; Harvard University; Harvard University
摘要：We define a Levy process on a d-dimensional hierarchical lattice. By construction the Green's function for this process decays as \x\2-d . For d = 4, we prove that the introduction of a sufficiently weak self-avoidance interaction does not change this decay provided the mass = killing rate is chosen in a special way, so that the process is critical.
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作者：SCHINAZI, R
摘要：We apply an invariance principle due to De Masi, Ferrari, Goldstein and Wick to the edge process for critical reversible nearest-particle systems. Their result also gives an upper bound for the diffusion constant that we compute explicitly. A comparison between the movement of the edge, when the other particles are frozen, and a random walk allows us to find a lower bound for the diffusion constant. This shows that the right renormalization for the edge to converge to a nondegenerate Brownian ...
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作者：BERTOIN, J; LEJAN, Y
摘要：Let X be a Hunt process starting from a regular recurrent point 0 and nu a smooth probability measure on the state space. We show that T = inf{s: A(s) > L(s)}, where A is the continuous additive functional associated to nu and L the local time at 0, solves the Skorokhod problem for nu, that is, X(T) has law-nu. We construct another solution which minimizes E0(B(S)) among all the solutions S of the Skorokhod problem, where B is any positive continuous additive functional. The special case where...
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作者：BASAK, GK; BHATTACHARYA, RN
作者单位：Indiana University System; Indiana University Bloomington
摘要：A verifiable criterion is derived for the stability in distribution of singular diffusions, that is, for the weak convergence of the transition probability p(t; x, dy), as t --> infinity, to a unique invariant probability. For this we establish the following: (i) tightness of {p(t; x, dy): t greater-than-or-equal-to 0}; and (ii) asymptotic flatness of the stochastic flow. When specialized to highly nonradial nonsingular diffusions the results here are often applicable where Has'minskii's well-...
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作者：LYONS, R; PEMANTLE, R
作者单位：University of Wisconsin System; University of Wisconsin Madison; Stanford University; University of California System; University of California Berkeley
摘要：We show that the transience or recurrence of a random walk in certain random environments on an arbitrary infinite locally finite tree is determined by the branching number of the tree, which is a measure of the average number of branches per vertex. This generalizes and unifies previous work of the authors. It also shows that the point of phase transition for edge-reinforced random walk is likewise determined by the branching number of the tree. Finally, we show that the branching number dete...
