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作者：Roitershtein, Alexander
作者单位：University of British Columbia
摘要：We consider a multitype branching process with immigration in a random environment introduced by Key in [Ann. Probab. 15 (1987) 344-353]. It was shown by Key that, under the assumptions made in [Ann. Probab. 15 (1987) 344-353], the branching process is subcritical in the sense that it converges to a proper limit law. We complement this result by a strong law of large numbers and a central limit theorem for the partial sums of the process. In addition, we study the asymptotic behavior of oscill...
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作者：Nishiyama, Yoichi
作者单位：Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
摘要：This note extends some results of Nishiyama [Ann. Probab. 28 (2000) 685-712]. A maximal inequality for stochastic integrals with respect to integer-valued random measures which may have infinitely many jumps on compact time intervals is given. By using it, a tightness criterion is obtained; if the so-called quadratic modulus is bounded in probability and if a certain entropy condition on the parameter space is satisfied, then the tightness follows. Our approach is based on the entropy techniqu...
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作者：Randrianantoanina, Narcisse
作者单位：University System of Ohio; Miami University
摘要：We prove a weak-type (1, 1) inequality involving conditioned versions of square functions for martingales in noncommutative L-P-spaces associated with finite von Neumann algebras. As application, we determine the optimal orders for the best constants in the noncommutative Burkholder/Rosenthal inequalities from [Ann. Probab. 31 (2003) 948-995]. We also discuss BMO-norms of sums of noncommuting order-independent operators.
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作者：Wang, Feng-Yu
作者单位：Beijing Normal University
摘要：By using coupling and Girsanov transformations, the dimension-free Harnack inequality and the strong Feller property are proved for transition semigroups of solutions to a class of stochastic generalized porous media equations. As applications, explicit upper bounds of the L-P-norm of the density as well as hypercontractivity, ultracontractivity and compactness of the corresponding semigroup are derived.
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作者：Greven, A.; Den Hollander, F.
作者单位：University of Erlangen Nuremberg; Leiden University; Leiden University - Excl LUMC
摘要：Let ({X-i(t)}(i is an element of Z)(d))(t >= 0) be the system of interacting diffusions on [0, infinity) defined by the following collection of coupled stochastic differential equations: dX(i) (t) = Sigma(d)(j is an element of Z) a(i, j)[X-j(t) - X-i(t)]dt + root bX(i)(t)(2)dW(i)(t), i is an element of Z(d), t >= 0. Here, a(., .) is an irreducible random walk transition kernel on Z(d) x Z(d), b is an element of (0, infinity) is a diffusion parameter, and ({W-i(t)}(i is an element of Z)(d))(t >...
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作者：Ferrari, Pablo A.; Martin, James B.
作者单位：Universidade de Sao Paulo; University of Oxford
摘要：We consider totally asymmetric simple exclusion processes with n types of particle and holes (n-TASEPs) on Z and on the cycle Z(N). Angel recently gave an elegant construction of the stationary measures for the 2-TASEP, based on a pair of independent product measures. We show that Angel's construction can be interpreted in terms of the operation of a discrete-time M/M/1 queueing server; the two product measures correspond to the arrival and service processes of the queue. We extend this constr...
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作者：Wu, Wei Biao
作者单位：University of Chicago
摘要：We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated logarithm are also obtained under easily verifiable conditions.
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作者：Hu, Yueyun; Shi, Zhan
作者单位：Universite Paris 13; Universite Paris Cite; Sorbonne Universite
摘要：We consider a recurrent random walk in a random environment on a regular tree. Under suitable general assumptions concerning the distribution of the environment, we show that the walk exhibits an unusually slow movement: the order of magnitude of the walk in the first n steps is (log n)(3).
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作者：Doney, Ron; Maller, Ross
作者单位：University of Manchester; Australian National University; Australian National University
摘要：Let R-n = max(0 <= j <= n) S-j - S-n be a random walk S-n reflected in its maximum. Except in the trivial case when P(X >= 0) = 1, R-n will pass over a horizontal boundary of any height in a finite time, with probability 1. We extend this by giving necessary and sufficient conditions for finiteness of passage times of R-n above certain curved (power law) boundaries, as well. The intuition that a degree of heaviness of the negative tail of the distribution of the increments of S-n is necessary ...
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作者：Broman, Erik I.
作者单位：Chalmers University of Technology
摘要：The ordinary contact process is used to model the spread of a disease in a population. In this model, each infected individual waits an exponentially distributed time with parameter 1 before becoming healthy. In this paper, we introduce and study the contact process in a randomly evolving environment. Here we associate to every individual an independent two-state, {0, 1}, background process. Given delta(0) < delta(1), if the background process is in state 0, the individual (if infected) become...
