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作者：Bayer, Christian; Horst, Ulrich; Qiu, Jinniao
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Humboldt University of Berlin; University of Michigan System; University of Michigan
摘要：We consider a stochastic model for the dynamics of the two-sided limit order book (LOB). Our model is flexible enough to allow for a dependence of the price dynamics on volumes. For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a functional limit theorem, which states that our LOB model converges in distribution to a fully coupled SDE-SPDE system when the order arrival rates tend to infinity and the impact of an individual order arrival...
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作者：Laslier, Benoit; Laslier, Jean-Francois
作者单位：Universite Paris Cite; Paris School of Economics; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：This paper deals with two generalizations of the Polya urn model where, instead of sampling one ball from the urn at each time, we sample two or three balls. The processes are defined on the basis of the problem of finding the best alternative using pairwise comparisons which are not necessarily transitive: they can be thought of as evolutionary processes that tend to reinforce currently efficient alternatives. The two processes exhibit different behaviors: with three balls sampled, we prove a...
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作者：Feige, Uriel; Krivelevich, Michael; Reichman, Daniel
作者单位：Weizmann Institute of Science; Tel Aviv University; University of California System; University of California Berkeley
摘要：We consider the following activation process in undirected graphs: a vertex is active either if it belongs to a set of initially activated vertices or if at some point it has at least r active neighbors. A contagious set is a set whose activation results with the entire graph being active. Given a graph G, let m(G, r) be the minimal size of a contagious set. We study this process on the binomial random graph G := G(n, p) with p := d/n and 1 << d << (nloglogn/log(2)n )(r-1/r). Assuming r > 1 to...
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作者：Fournier, Nicolas; Jourdain, Benjamin
作者单位：Sorbonne Universite; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Inria; Universite Gustave-Eiffel
摘要：We are interested in the two-dimensional Keller-Segel partial differential equation. This equation is a model for chemotaxis (and for Newtonian gravitational interaction). When the total mass of the initial density is one, it is known to exhibit blow-up in finite time as soon as the sensitivity chi of bacteria to the chemo-attractant is larger than 8 pi. We investigate its approximation by a system of N two-dimensional Brownian particles interacting through a singular attractive kernel in the ...
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作者：Grigorova, Miryana; Imkeller, Peter; Offen, Elias; Ouknine, Youssef; Quenez, Marie-Claire
作者单位：Humboldt University of Berlin; University of Botswana; Cadi Ayyad University of Marrakech; Universite Paris Cite
摘要：In the first part of the paper, we study reflected backward stochastic differential equations (RBSDEs) with lower obstacle which is assumed to be right upper-semicontinuous but not necessarily right-continuous. We prove existence and uniqueness of the solutions to such RBSDEs in appropriate Banach spaces. The result is established by using some results from optimal stopping theory, some tools from the general theory of processes such as Mertens' decomposition of optional strong supermartingale...
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作者：Bhamidi, Shankar; Van der Hofstad, Remco; Hooghiemstra, Gerard
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Eindhoven University of Technology; Delft University of Technology
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作者：Buckdahn, Rainer; Li, Juan; Ma, Jin
作者单位：Universite de Bretagne Occidentale; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Shandong University; Shandong University; University of Southern California
摘要：In this paper, we are interested in a new type of mean-field, non-Markovian stochastic control problems with partial observations. More precisely, we assume that the coefficients of the controlled dynamics depend not only on the paths of the state, but also on the conditional law of the state, given the observation to date. Our problem is strongly motivated by the recent study of the mean field games and the related McKean-Vlasov stochastic control problem, but with added aspects of path-depen...
