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作者：Raimond, Olivier; Schapira, Bruno
作者单位：Universite Paris Saclay; Universite Paris Saclay; Universite Paris Nanterre
摘要：We obtain the convergence in law of a sequence of excited (also called cookies) random walks toward an excited Brownian motion. This last process is a continuous semi-martingale whose drift is a function, say phi, of its local time. It was introduced by Norris, Rogers and Williams as a simplified version of Brownian polymers, and then recently further studied by the authors. To get our results we need to renormalize together the sequence of cookies, the time and the space in a convenient way. ...
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作者：Horvath, Illes; Toth, Balint; Veto, Balint
作者单位：Budapest University of Technology & Economics
摘要：The problems considered in the present paper have their roots in two different cultures. The `true' (or myopic) self-avoiding walk model (TSAW) was introduced in the physics literature by Amit et al. (Phys Rev B 27:1635-1645, 1983). This is a nearest neighbor non-Markovian random walk in which prefers to jump to those neighbors which were less visited in the past. The self-repelling Brownian polymer model (SRBP), initiated in the probabilistic literature by Durrett and Rogers (Probab Theory Re...
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作者：Bakry, Dominique; Bolley, Francois; Gentil, Ivan
作者单位：Universite PSL; Universite Paris-Dauphine; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We derive sharp, local and dimension dependent hypercontractive bounds on the Markov kernel of a large class of diffusion semigroups. Unlike the dimension free ones, they capture refined properties of Markov kernels, such as trace estimates. They imply classical bounds on the Ornstein-Uhlenbeck semigroup and a dimensional and refined (transportation) Talagrand inequality when applied to the Hamilton-Jacobi equation. Hypercontractive bounds on the Ornstein-Uhlenbeck semigroup driven by a non-di...
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作者：Nutz, Marcel
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider the economic problem of optimal consumption and investment with power utility. We study the optimal strategy as the relative risk aversion tends to infinity or to one. The convergence of the optimal consumption is obtained for general semimartingale models while the convergence of the optimal trading strategy is obtained for continuous models. The limits are related to exponential and logarithmic utility. To derive these results, we combine approaches from optimal control, convex a...
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作者：Aistleitner, Christoph; Fukuyama, Katusi
作者单位：Graz University of Technology; Kobe University
摘要：Let (n(k)) k >= 1 be an increasing sequence of positive integers. Bobkov and Gotze proved that if the distribution of cos 2 pi n(1)x + ... + cos 2 pi nNx/root N converges to a Gaussian distribution, then the value of the variance is bounded from above by 1/2 - lim sup k/(2n(k)). In particular it is impossible that for a sequence (n(k)) k >= 1 with bounded gaps (i.e. n(k+1) - n(k) <= c for some constant c) the distribution of (1) converges to a Gaussian distribution with variance sigma(2) = 1/2...
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作者：Conus, Daniel; Khoshnevisan, Davar
作者单位：Utah System of Higher Education; University of Utah
摘要：We study the stochastic heat equation partial derivative(t)u = Lu + sigma(u)(W) over dot in (1 + 1) dimensions, where (W) over dot is space-time white noice sigma : R -> R is Lipschitz continuous, and L is the generator of a symmetric L,vy process that has finite exponential moments, and u (0) has exponential decay at +/- a. We prove that under natural conditions on sigma : (i) The nu th absolute moment of the solution to our stochastic heat equation grows exponentially with time; and (ii) The...
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作者：Mikulevicius, R.; Rozovskii, B. L.
作者单位：Brown University; University of Southern California
摘要：A random perturbation of a deterministic Navier-Stokes equation is considered in the form of an SPDE with Wick type nonlinearity. The nonlinear term of the perturbation can be characterized as the highest stochastic order approximation of the original nonlinear term . This perturbation is unbiased in that the expectation of a solution of the perturbed equation solves the deterministic Navier-Stokes equation. The perturbed equation is solved in the space of generalized stochastic processes usin...
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作者：Beffara, Vincent; Duminil-Copin, Hugo
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); University of Geneva
摘要：We prove a long-standing conjecture on random-cluster models, namely that the critical point for such models with parameter q a parts per thousand yen 1 on the square lattice is equal to the self-dual point . This gives a proof that the critical temperature of the q-state Potts model is equal to for all q a parts per thousand yen 2. We further prove that the transition is sharp, meaning that there is exponential decay of correlations in the sub-critical phase. The techniques of this paper are ...
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作者：Osada, Hirofumi
作者单位：Kyushu University
摘要：We solve infinite-dimensional stochastic differential equations (ISDEs) describing an infinite number of Brownian particles interacting via two-dimensional Coulomb potentials. The equilibrium states of the associated unlabeled stochastic dynamics are the Ginibre random point field and Dyson's measures, which appear in random matrix theory. To solve the ISDEs we establish an integration by parts formula for these measures. Because the long-range effect of two-dimensional Coulomb potentials is q...
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作者：Pitman, Jim; Ross, Nathan
作者单位：University of California System; University of California Berkeley
摘要：This article contains both a point process and a sequential description of the greatest convex minorant of Brownian motion on a finite interval. We use these descriptions to provide new analysis of various features of the convex minorant such as the set of times where the Brownian motion meets its minorant. The equivalence of these descriptions is non-trivial, which leads to many interesting identities between quantities derived from our analysis. The sequential description can be viewed as a ...
