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作者：Belomestny, Denis; Kraetschmer, Volker
作者单位：University of Duisburg Essen; HSE University (National Research University Higher School of Economics)
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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：Amir, Gideon; Angel, Omer; Kozma, Gady
作者单位：Bar Ilan University; University of British Columbia; Weizmann Institute of Science
摘要：We examine diffusion-limited aggregation for a one-dimensional random walk with long jumps. We achieve upper and lower bounds on the growth rate of the aggregate as a function of the number of moments a single step of the walk has. In this paper, we handle the case of transient walks.
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作者：Yu, Xiang
作者单位：Hong Kong Polytechnic University
摘要：This paper studies the optimal consumption via the habit formation preference in markets with transaction costs and unbounded random endowments. To model the proportional transaction costs, we adopt the Kabanov's multi asset framework with a cash account. At the terminal time T, the investor can receive unbounded random endowments for which we propose a new definition of acceptable portfolios based on the strictly consistent price system (SCPS). We prove a type of super-hedging theorem using t...
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作者：Ley, Christophe; Reinert, Gesine; Swan, Yvik
作者单位：Ghent University; University of Oxford; University of Liege
摘要：this paper, we propose tight upper and lower bounds for the Wasser-stein distance between any two univariate continuous distributions with probability densities p(1) and p(2) having nested supports. These explicit bounds are expressed in terms of the derivative of the likelihood ratio p(1)/p(2) as well as the Stein kernel tau(1) of p(1). The method of proof relies on a new variant of Stein's method which manipulates Stein operators. We give several applications of these bounds. Our main applic...
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作者：Karnam, Chandrasekhar; Ma, Jin; Zhang, Jianfeng
作者单位：University of Southern California
摘要：In this paper, we investigate possible approaches to study general time-inconsistent optimization problems without assuming the existence of optimal strategy. This leads immediately to the need to refine the concept of time consistency as well as any method that is based on Pontryagin's maximum principle. The fundamental obstacle is the dilemma of having to invoke the Dynamic Programming Principle (DPP) in a time-inconsistent setting, which is contradictory in nature. The main contribution of ...
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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：Clement, Emmanuelle; Gloter, Arnaud
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：It is well known that the strong error approximation in the space of continuous paths equipped with the supremum norm between a diffusion process, with smooth coefficients, and its Euler approximation with step 1/n is O(n(-1/2)) and that the weak error estimation between the marginal laws at the terminal time T is O(n(-1)). An analysis of the weak trajectorial error has been developed by Alfonsi, Jourdain and Kohatsu-Higa [Ann. Appl. Probab. 24 (2014) 1049-1080], through the study of the p-Was...
