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作者：Bovier, Anton; Coquille, Loren; Smadi, Charline
作者单位：University of Bonn; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); INRAE; Universite Paris Cite
摘要：We consider a stochastic model of population dynamics where each individual is characterised by a trait in {0, 1, . . . , L} and has a natural reproduction rate, a logistic death rate due to age or competition and a probability of mutation towards neighbouring traits at each reproduction event. We choose parameters such that the induced fitness landscape exhibits a valley: mutant individuals with negative fitness have to be created in order for the population to reach a trait with positive fit...
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作者：Schlichting, Andre; Slowik, Martin
作者单位：University of Bonn; Technical University of Berlin
摘要：We investigate the metastable behavior of reversible Markov chains on possibly countable infinite state spaces. Based on a new definition of metastable Markov processes, we compute precisely the mean transition time between metastable sets. Under additional size and regularity properties of metastable sets, we establish asymptotic sharp estimates on the Poincare and logarithmic Sobolev constant. The main ingredient in the proof is a capacitary inequality along the lines of V. Maz'ya that relat...
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作者：Nam, Danny; Nestoridi, Evita
作者单位：Princeton University
摘要：We study the cyclic adjacent transposition (CAT) shuffle of n cards, which is a systematic scan version of the random adjacent transposition (AT) card shuffle. In this paper, we prove that the CAT shuffle exhibits cutoff at n(3)/2 pi(2) log n, which concludes that it is twice as fast as the AT shuffle. This is the first verification of cutoff phenomenon for a time-inhomogeneous card shuffle.
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作者：Viens, Frederi; Zhang, Jianfeng
作者单位：Michigan State University; University of Southern California
摘要：In this paper, we study dynamic backward problems, with the computation of conditional expectations as a special objective, in a framework where the (forward) state process satisfies a Volterra type SDE, with fractional Brownian motion as a typical example. Such processes are neither Markov processes nor semimartingales, and most notably, they feature a certain time inconsistency which makes any direct application of Markovian ideas, such as flow properties, impossible without passing to a pat...
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作者：Bayraktar, Erhan; Cvitanic, Jaksa; Zhang, Yuchong
作者单位：University of Michigan System; University of Michigan; California Institute of Technology; University of Toronto
摘要：We consider a stochastic tournament game in which each player is rewarded based on her rank in terms of the completion time of her own task and is subject to cost of effort. When players are homogeneous and the rewards are purely rank dependent, the equilibrium has a surprisingly explicit characterization, which allows us to conduct comparative statics and obtain explicit solution to several optimal reward design problems. In the general case when the players are heterogenous and payoffs are n...
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作者：Gong, Ruoting; Mou, Chenchen; Swiech, Andrzej
作者单位：Illinois Institute of Technology; University of California System; University of California Los Angeles; University System of Georgia; Georgia Institute of Technology
摘要：We prove a stochastic representation formula for the viscosity solution of Dirichlet terminal-boundary value problem for a degenerate Hamilton- Jacobi-Bellman integro-partial differential equation in a bounded domain. We show that the unique viscosity solution is the value function of the associated stochastic optimal control problem. We also obtain the dynamic programming principle for the associated stochastic optimal control problem in a bounded domain.
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作者：Kliem, Sandra
作者单位：Goethe University Frankfurt
摘要：We consider the one-dimensional KPP-equation driven by space-time white noise. We show that for all parameters above the critical value for survival, there exist stochastic wavelike solutions which travel with a deterministic positive linear speed. We further give a sufficient condition on the initial condition of a solution to attain this speed. Our approach is in the spirit of corresponding results for the nearest-neighbor contact process respectively oriented percolation. Here, the main dif...
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作者：Bank, Peter; Dolinsky, Yan
作者单位：Technical University of Berlin; Hebrew University of Jerusalem; Monash University
摘要：We establish a superreplication duality in a continuous-time financial model as in (Bank and Vo beta (2018)) where an investor's trades adversely affect bid- and ask-prices for a risky asset and where market resilience drives the resulting spread back towards zero at an exponential rate Similar to the literature on models with a constant spread (cf., e.g., Math. Finance 6 (1996) 133-165; Ann. Appl. Probab. 20 (2010) 1341-1358; Ann. Appl. Probab. 27 (2017) 1414-1451), our dual description of su...
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作者：Broeker, Yannic; Mukherjee, Chiranjib
作者单位：University of Munster
摘要：We consider a Gaussian multiplicative chaos (GMC) measure on the classical Wiener space driven by a smoothened (Gaussian) space-time white noise. For d >= 3, it was shown in (Electron. Commun. Probab. 21 (2016) 61) that for small noise intensity, the total mass of the GMC converges to a strictly positive random variable, while larger disorder strength (i.e., low temperature) forces the total mass to lose uniform integrability, eventually producing a vanishing limit. Inspired by strong localiza...
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作者：Todorov, Viktor
作者单位：Northwestern University
摘要：We propose a nonparametric estimator of spot volatility from noisy short-dated option data. The estimator is based on forming portfolios of options with different strikes that replicate the (risk-neutral) conditional characteristic function of the underlying price in a model-free way. The separation of volatility from jumps is done by making use of the dominant role of the volatility in the conditional characteristic function over short time intervals and for large values of the characteristic...
