-
作者：Trillos, Camilo Andres Garcia
作者单位：Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
摘要：We propose an algorithm for approximating the solution of a strongly oscillating SDE, that is, a system in which some ergodic state variables evolve quickly with respect to the other variables. The algorithm profits from homogenization results and consists of an Euler scheme for the slow scale variables coupled with a decreasing step estimator for the ergodic averages of the quick variables. We prove the strong convergence of the algorithm as well as a C.L.T. like limit result for the normaliz...
-
作者：Bally, Vlad; Kohatsu-Higa, Arturo
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Inria; Ritsumeikan University; Japan Science & Technology Agency (JST)
摘要：In this article, we introduce the parametrix technique in order to construct fundamental solutions as a general method based on semigroups and their generators. This leads to a probabilistic interpretation of the parametrix method that is amenable to Monte Carlo simulation. We consider the explicit examples of continuous diffusions and jump driven stochastic differential equations with Holder continuous coefficients.
-
作者：Ferrari, Giorgio
作者单位：University of Bielefeld
摘要：In this paper, we derive a new handy integral equation for the freeboundary of infinite time horizon, continuous time, stochastic, irreversible investment problems with uncertainty modeled as a one-dimensional, regular diffusion X. The new integral equation allows to explicitly find the freeboundary b(.) in some so far unsolved cases, as when the operating profit function is not multiplicatively separable and X is a three-dimensional Bessel process or a CEV process. Our result follows from pur...
-
作者：Possamai, Dylan; Tan, Xiaolu
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：We study the weak approximation of the second-order backward SDEs (2BSDEs), when the continuous driving martingales are approximated by discrete time martingales. We establish a convergence result for a class of 2BSDEs, using both robustness properties of BSDEs, as proved in Briand, Delyon and Memin [Stochastic Process. Appl. 97 (2002) 229-253], and tightness of solutions to discrete time BSDEs. In particular, when the approximating martingales are given by some particular controlled Markov ch...
-
作者：Jansen, Sabine; Koenig, Wolfgang; Metzger, Bernd
作者单位：Ruhr University Bochum; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technical University of Berlin
摘要：An interesting problem in statistical physics is the condensation of classical particles in droplets or clusters when the pair-interaction is given by a stable Lennard Jones-type potential. We study two aspects of this problem. We start by deriving a large deviations principle for the cluster size distribution for any inverse temperature beta is an element of (0, infinity) and particle density rho is an element of (0, rho(cp)) in the thermodynamic limit. Here rho(cp) > 0 is the close packing d...
-
作者：Perl, Idan; Sen, Arnab; Yadin, Ariel
作者单位：Ben-Gurion University of the Negev; University of Minnesota System; University of Minnesota Twin Cities
摘要：We study a model of growing population that competes for resources. At each time step, all existing particles reproduce and the offspring randomly move to neighboring sites. Then at any site with more than one offspring, the particles are annihilated. This is a nonmonotone model, which makes the analysis more difficult. We consider the extinction window of this model in the finite mean-field case, where there are n sites but movement is allowed to any site (the complete graph). We show that al...
-
作者：Henard, Olivier
作者单位：University of London; Queen Mary University London
摘要：We define a Markov process in a forward population model with backward genealogy given by the Lambda-coalescent. This Markov process, called the fixation line, is related to the block counting process through its hitting times. Two applications are discussed. The probability that the n-coalescent is deeper than the (n - 1)-coalescent is studied. The distribution of the number of blocks in the last coalescence of the n-Beta(2 - alpha, alpha)-coalescent is proved to converge as n -> infinity, an...
-
作者：Dieuleveut, Daphne
作者单位：Universite Paris Saclay
摘要：We consider a fragmentation of discrete trees where the internal vertices are deleted independently at a rate proportional to their degree. Informally, the associated cut-tree represents the genealogy of the nested connected components created by this process. We essentially work in the setting of Galton-Watson trees with offspring distribution belonging to the domain of attraction of a stable law of index alpha is an element of (1, 2). Our main result is that, for a sequence of such trees T-n...
-
作者：Jourdain, Benjamin; Lelievre, Tony; Miasojedow, Blazej
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Inria; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; University of Warsaw
摘要：We consider the random walk Metropolis algorithm on R-n with Gaussian proposals, and when the target probability measure is the n-fold product of a one-dimensional law. In the limit n -> infinity, it is well known (see [Ann. Appl. Probab. 7 (1997) 110-120]) that, when the variance of the proposal scales inversely proportional to the dimension n whereas time is accelerated by the factor n, a diffusive limit is obtained for each component of the Markov chain if this chain starts at equilibrium. ...
-
作者：Chi, Zhiyi
作者单位：University of Connecticut
摘要：Let F be a distribution function on the line in the domain of attraction of a stable law with exponent alpha is an element of (0,1/2]. We establish the strong renewal theorem for a random walk S-1, S-2, ... with step distribution F, by extending the large deviations approach in Doney [Probab. Theory Related Fileds 107 (1997) 451-465]. This is done by introducing conditions on F that in general rule out local large deviations bounds of the type P{S-n is an element of(x, x + h]} = O(n)(F) over b...
