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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...
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作者：Basu, Riddhipratim; Sly, Allan
作者单位：Stanford University; University of California System; University of California Berkeley
摘要：In this paper, we examine a variant of the voter model on a dynamically changing network where agents have the option of changing their friends rather than changing their opinions. We analyse, in the context of dense random graphs, two models considered in Durrett et al. [Proc. Natl. Acad. Sci. USA 109 (2012) 3682-3687]. When an edge with two agents holding different opinion is updated, with probability &, one agent performs a voter model step and changes its opinion to copy the other, and wit...
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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...
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作者：Watanabe, Shun; Hayashi, Masahito
作者单位：Tokyo University of Agriculture & Technology; Nagoya University; National University of Singapore
摘要：Using terminologies of information geometry, we derive upper and lower bounds of the tail probability of the sample mean for the Markov chain with finite state space. Employing these bounds, we obtain upper and lower bounds of the minimum error probability of the type-2 error under the exponential constraint for the error probability of the type-1 error in a simple hypothesis testing for a finite-length Markov chain, which yields the Hoeffding-type bound. For these derivations, we derive upper...
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作者：Arguin, Louis-Pierre; Belius, David; Harper, Adam J.
作者单位：Universite de Montreal; City University of New York (CUNY) System; Baruch College (CUNY); City University of New York (CUNY) System; New York University
摘要：A recent conjecture of Fyodorov-Hiary-Keating states that the maximum of the absolute value of the Riemann zeta function on a typical bounded interval of the critical line is exp{loglogT - 3/4logloglogT + O(1)}, for an interval at (large) height T. In this paper, we verify the first two terms in the exponential for a model of the zeta function, which is essentially a randomized Euler product. The critical element of the proof is the identification of an approximate tree structure, present also...
