-
作者：Kious, Daniel; Mailler, Cecile; Schapira, Bruno
作者单位：University of Bath; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：It is well known in biology that ants are able to find shortest paths between their nest and the food by successive random explorations, without any mean of communication other than the pheromones they leave behind them. This striking phenomenon has been observed experimentally and modelled by different mean-field reinforcement-learning models in the biology literature. In this paper, we introduce the first probabilistic reinforcement-learning model for this phenomenon. In this model, the ants...
-
作者：Dhara, Souvik; Sen, Subhabrata
作者单位：Massachusetts Institute of Technology (MIT); Harvard University
摘要：Consider the random graph sampled uniformly from the set of all simple graphs with a given degree sequence. Under mild conditions on the degrees, we establish a large deviation principle (LDP) for these random graphs, viewed as elements of the graphon space. As a corollary of our result, we obtain LDPs for functionals continuous with respect to the cut metric, and obtain an asymptotic enumeration formula for graphs with given degrees, subject to an additional constraint on the value of a conti...
-
作者：Christensen, Soeren; Kallsen, Jan; Lenga, Matthias
作者单位：University of Kiel; Bayer AG
摘要：We call a given American option representable if there exists a European claim which dominates the American payoff at any time and such that the values of the two options coincide in the continuation region of the American option. This concept has interesting implications from a probabilistic, analytic, financial, and numeric point of view. Relying on methods from (Math. Finance 24 (2014) 156-172; Ann. Inst. H. Poincare Anal. Non Lineaire 18 (2001) 1-17; Ann. Appl. Probab. 12 (2002) 196-223) a...
-
作者：Motte, Mederic; Huyen Pham
作者单位：Universite Paris Cite
摘要：We develop an exhaustive study of Markov decision process (MDP) under mean field interaction both on states and actions in the presence of common noise, and when optimization is performed over open-loop controls on infinite horizon. Such model, called CMKV-MDP for conditional McKean- Vlasov MDP, arises and is obtained here rigorously with a rate of convergence as the asymptotic problem of N-cooperative agents controlled by a social planner/influencer that observes the environment noises but no...
-
作者：Yin, Yanqing; Ma, Yanyuan
作者单位：Chongqing University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：This paper is to study the properties of eigenvalues and eigenvectors of high-dimensional sample correlation matrices. We first improve the result of Jiang (Sankhya over bar 66 (2004) 35-48), Xiao and Zhou (J. Theoret. Probab. 23 (2010) 1-20) and the Theorem 1 of El Karoui (Ann. Appl. Probab. 19 (2009) 2362-2405), both concerning the limiting spectral distribution and the ex-treme eigenvalues of sample correlation matrices, by allowing a more general fourth moment condition. Then, we establish...
-
作者：Kallblad, Sigrid
作者单位：Royal Institute of Technology
摘要：We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales enables us to transform the distributional constraint into an initial condition and view the problem as a stochastic control problem; we establish the corresponding dynamic programming principle. The method offers a systematic approach for solving the problem for general constraints and under weak assumptions o...
-
作者：Olesker-Taylor, Sam
作者单位：University of Bath
摘要：Consider N stations interconnected with links, each of capacity K, forming a complete graph. Calls arrive to each link at rate lambda and depart at rate 1. If a call arrives to a link xy, connecting stations x and y, which is at capacity, then a third station z is chosen uniformly at random and the call is attempted to be routed via z: if both links xz and zy have spare capacity, then the call is held simultaneously on these two; otherwise the call is lost. We analyse an approximation of this ...
-
作者：Jorritsma, Joost; Komjathy, Julia
作者单位：Eindhoven University of Technology; Delft University of Technology
摘要：We study the evolution of the graph distance and weighted distance between two fixed vertices in dynamically growing random graph models. More precisely, we consider preferential attachment models with power -law exponent tau e (2, 3), sample two vertices ut, vt uniformly at random when the graph has t vertices and study the evolution of the graph dis-tance between these two fixed vertices as the surrounding graph grows. This yields a discrete-time stochastic process in t' > t, called the dis-...
-
作者：Fang, Rongjuan; Li, Zenghu
作者单位：Fujian Normal University; Beijing Normal University
摘要：A continuous-state branching process in varying environments is constructed by the pathwise unique positive solution to a stochastic integral equation driven by time-space noises. The cumulant semigroup of the process is characterized in terms of a backward integral equation. We clarify the behavior of the process at its bottlenecks, which are the deterministic times when it arrives at zero almost surely by negative jumps. The process arises naturally as the scaling limit of Galton-Watson proc...
-
作者：Fountoulakis, Nikolaos; Iyer, Tejas; Mailler, Cecile; Sulzbach, Henning
作者单位：University of Birmingham; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Bath
摘要：We study a general model of random dynamical simplicial complexes and derive a formula for the asymptotic degree distribution. This asymptotic formula generalises results for a number of existing models, including random Apollonian networks and the weighted random recursive tree. It also confirms results on the scale-free nature of complex quantum network manifolds in dimensions d > 2, and special types of network geometry with Flavour models studied in the physics literature by Bianconi and R...
