The Annals of Probability

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• Phase transitions for the long-time behavior of interacting diffusions AI翻译
  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 >...
• Stationary distributions of multi-type totally asymmetric exclusion processes AI翻译
  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...
• Strong invariance principles for dependent random variables AI翻译
  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.
• Slow movement of random walk in random environment on a regular tree AI翻译
  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).
• Curve crossing for random walks reflected at their maximum AI翻译
  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 ...
• Stochastic domination for a hidden markov chain with applications to the contact process in a randomly evolving environment AI翻译
  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...
• On the structure of general mean-variance hedging strategies AI翻译
  作者：Cerny, Ales; Kallsen, Jan
  作者单位：City St Georges, University of London; Technical University of Munich; Aalto University
  摘要：We provide a new characterization of mean-variance hedging strategies in a general semimartingale market. The key point is the introduction of a new probability measure P* which turns the dynamic asset allocation problem into a myopic one. The minimal martingale measure relative to P* coincides with the variance-optimal martingale measure relative to the original probability measure P.
• Multidimensional branching random walks in random environment AI翻译
  作者：Comets, Francis; Popov, Serguei
  作者单位：Universite Paris Cite; Universidade de Sao Paulo
  摘要：We study branching random walks in random i.i.d. environment in Z(d), d >= 1. For this model, the population size cannot decrease, and a natural definition of recurrence is introduced. We prove a dichotomy for recurrence/transience, depending only on the support of the environmental law. We give sufficient conditions for recurrence and for transience. In the recurrent case, we study the asymptotics of the tail of the distribution of the hitting times and prove a shape theorem for the set of la...
• On time-inhomogeneous controlled diffusion processes in domains AI翻译
  作者：Dong, Hongjie; Krylov, N. V.
  作者单位：University of Minnesota System; University of Minnesota Twin Cities
  摘要：Time-inhomogeneous controlled diffusion processes in both cylindrical and noncylindrical domains are considered. Bellman's principle and its applications to proving the continuity of value functions are investigated.
• Reflecting a langevin process at an absorbing boundary AI翻译
  作者：Bertoin, Jean
  作者单位：Sorbonne Universite; Universite Paris Cite; Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
  摘要：We consider a Langevin process with white noise random forcing. We suppose that the energy of the particle is instantaneously absorbed when it hits some fixed obstacle. We show that nonetheless, the particle can be instantaneously reflected, and study some properties of this reflecting solution.