-
作者：McSweeney, John K.; Popovic, Lea
作者单位：Rose Hulman Institute Technology; Concordia University - Canada
摘要：We study a stochastic two-species chemical reaction system with two mechanisms. One mechanism consists of chemical interactions which govern the overall drift of species amounts in the system; the other mechanism consists of resampling, branching or splitting which makes unbiased perturbative changes to species amounts. Our results show that in a system with a large but bounded capacity, certain combinations of these two types of interactions can lead to stochastically-induced bistability. Dep...
-
作者：Alfonsi, A.; Jourdain, B.; Kohatsu-Higa, A.
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Ritsumeikan University; Japan Science & Technology Agency (JST)
摘要：In the present paper, we prove that the Wasserstein distance on the space of continuous sample-paths equipped with the supremum norm between the laws of a uniformly elliptic one-dimensional diffusion process and its Eu ler discretization with N steps is smaller than O(N-2/3+epsilon) where epsilon is an arbitrary positive constant. This rate is intermediate between the strong error estimation in O(N-1/2) obtained when coupling the stochastic differential equation and the Euler scheme with the s...
-
作者：Touboul, Jonathan
作者单位：Universite PSL; College de France
摘要：We consider the problem of the limit of bio-inspired spatially extended neuronal networks including an infinite number of neuronal types (space locations), with space-dependent propagation delays modeling neural fields. The propagation of chaos property is proved in this setting under mild assumptions on the neuronal dynamics, valid for most models used in neuroscience, in a mesoscopic limit, the neural-field limit, in which we can resolve the quite fine structure of the neuron's activity in s...
-
作者：Briand, Philippe; Labart, Celine
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP); Universite Savoie Mont Blanc; CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We present an algorithm to solve BSDEs based on Wiener chaos expansion and Picard's iterations. We get a forward scheme where the conditional expectations are easily computed thanks to chaos decomposition formulas. We use the Malliavin derivative to compute Z. Concerning the error, we derive explicit bounds with respect to the number of chaos and the discretization time step. We also present numerical experiments. We obtain very encouraging results in terms of speed and accuracy.
-
作者：Borodin, Alexei; Corwin, Ivan
作者单位：Massachusetts Institute of Technology (MIT); Kharkevich Institute for Information Transmission Problems of the RAS
摘要：We study the parabolic Anderson model in (1 + 1) dimensions with nearest neighbor jumps and space time white noise (discrete space/continuous time). We prove a contour integral formula for the second moment and compute the second moment Lyapunov exponent. For the model with only jumps to the right, we prove a contour integral formula for all moments and compute moment Lyapunov exponents of all orders.
-
作者：Gruebel, Rudolf
作者单位：Leibniz University Hannover
摘要：We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces converge with probability 1. This is then used to obtain almost sure convergence for various tree functionals, together with representations of the respective limit random variables as functions of the limit tree.
-
作者：Ball, Frank G.; Sirl, David J.; Trapman, Pieter
作者单位：University of Nottingham; Loughborough University; Stockholm University
摘要：In this paper we consider a model for the spread of a stochastic SIR (Susceptible -> Infectious -> Recovered) epidemic on a network of individuals described by a random intersection graph. Individuals belong to a random number of cliques, each of random size, and infection can be transmitted between two individuals if and only if there is a clique they both belong to. Both the clique sizes and the number of cliques an individual belongs to follow mixed Poisson distributions. An infinite-type b...
-
作者：Rosenbaum, Mathieu; Tankov, Peter
作者单位：Sorbonne Universite; Universite Paris Cite; Universite Paris Cite
摘要：In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis with Financial Applications (2011) 331-346 Birkhauser/Springer Basel AG] for continuous processes, we propose a framework enabling us to (asymptotically) optimize the discretization times. More precisely, a discretization rule is said to be optimal if for a given cost function, no strategy has (asymptotically, for large cost) a lower mean...
-
作者：Jin, Baisuo; Wang, Chen; Bai, Z. D.; Nair, K. Krishnan; Harding, Matthew
作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS; National University of Singapore; Northeast Normal University - China; Northeast Normal University - China; Stanford University; Stanford University
摘要：This paper studies the limiting spectral distribution (LSD) of a symmetrized auto-cross covariance matrix. The auto-cross covariance matrix is defined as M-tau = 1/2T Sigma(T)(j=1) (e(j) e(j+tau)*+ e(j+tau)e(j)*) where e(j) is an N dimensional vectors of independent standard complex components with properties stated in Theorem 1.1, and tau is the lag. M-0 is well studied in the literature whose LSD is the Mareenko-Pastur (MP) Law. The contribution of this paper is in determining the LSD of M-t...
-
作者：Ouchard, Bruno B.; Moreau, Ludovic; Nutz, Marcel
作者单位：Universite PSL; Universite Paris-Dauphine; Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris; Swiss Federal Institutes of Technology Domain; ETH Zurich; Columbia University
摘要：We study a stochastic game where one player tries to find a strategy such that the state process reaches a target of controlled-loss-type, no matter which action is chosen by the other player. We provide, in a general setup, a relaxed geometric dynamic programming principle for this problem and derive, for the case of a controlled SDE, the corresponding dynamic programming equation in the sense of viscosity solutions. As an example, we consider a problem of partial hedging under Knightian unce...
