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作者：Baker, Graeme; Shkolnikov, Mykhaylo
作者单位：Columbia University; Carnegie Mellon University
摘要：We consider a probabilistic formulation of a singular two-phase Stefan problem in one space dimension, which amounts to a coupled system of two McKean-Vlasov stochastic differential equations. In the financial context of systemic risk, this system models two competing regions with a large number of interconnected banks or firms at risk of default. Our main result shows the existence of a solution whose discontinuities obey the natural physicality condition for the problem at hand. Thus, this w...
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作者：Imkeller, Peter; Pellat, Rhoss likibi; Menoukeu-pamen, Olivier
作者单位：Humboldt University of Berlin; University of Liverpool
摘要：In this paper, we consider quadratic forward-backward SDEs (QFBSDEs), for which the drift in the forward equation does not satisfy the standard globally Lipschitz condition and the driver of the backward system possesses nonlinearity of type f (|y|)|z|2, where f is any locally integrable function. We prove both the Malliavin and classical differentiability of solutions to this type of QFBSDEs and provide representations of these derivatives processes. As a by-product, we derive a representatio...
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作者：Thuan, Nguyen tran
作者单位：Saarland University; Vinh University
摘要：This article investigates discrete-time approximations of stochastic integrals driven by semimartingales with jumps via weighted bounded mean osfor the approximation error depending on the weight, and it allows a change of the underlying measure which leaves the error estimates unchanged. To take advantage of this approach, we propose a new approximation scheme obtained from an adjustment for the Riemann approximation based on tracking jumps of the underlying semimartingale. We discuss a way t...
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作者：Hocquet, Antoine; Neamtu, Alexandra
作者单位：Technical University of Berlin; University of Konstanz
摘要：We investigate the abstract Cauchy problem for a quasilinear parabolic equation in a Banach space of the form dut - Lt(ut)ut dt = Nt(ut)dt + F(ut) d X t , where X is a gamma-H & ouml;lder rough path for gamma E ( 1 / 3 , 1/2). We explore the mild formulation that combines functional analysis techniques and controlled rough paths theory which entail the local well-posedness of such equations. We apply our results to the stochastic Landau-Lifshitz-Gilbert and Shigesada-Kawasaki-Teramoto equation.
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作者：Pymar, Richard; Rivera, Nicolas
作者单位：University of London; University of Greenwich; Universidad de Valparaiso
摘要：Given a transition matrix P indexed by a finite set V of vertices, the voter model is a discrete-time Markov chain in {0, 1}V where at each time-step a randomly chosen vertex x imitates the opinion of vertex y with probability P(x, y). The noisy voter model is a variation of the voter model in which vertices may change their opinions by the action of an external noise. The strength of this noise is measured by an extra parameter p is an element of [0, 1]. In this work we analyse the density pr...
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作者：Zhou, Jianjun
作者单位：Northwest A&F University - China
摘要：This paper introduces a notion of viscosity solutions for second order elated with infinite-horizon optimal control problems for stochastic differential equations with infinite delay. We identify the value functional of optimal control problems as unique viscosity solution to associated second order elliptic HJB equations with infinite delay. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions, and satisfies a stability property.
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作者：Li, Liping; Sun, Wenjie
作者单位：Fudan University; Tongji University
摘要：In this paper we study a stiff problem in two-dimensional space and especially characterize its probabilistic counterpart. More specifically, consider the heat equation with a parameter epsilon > 0: partial derivative(t)u(epsilon)(t,x) = 1/2 del (A(epsilon) (x)del u(epsilon)(t,x)), t >= 0 , x is an element of R-2, where A(epsilon) (x) := Id(2), the identity matrix, for x is not an element of Omega(epsilon) := { x = (x(1),x(2)) is an element of R-2: |x(2) | < epsilon } and A(epsilon) (x) := (a(...
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作者：Banderier, Cyril; Kuba, Markus; Wallner, Michael
作者单位：Universite Paris 13; Technische Universitat Wien; Technische Universitat Wien
摘要：Multitudinous probabilistic and combinatorial objects are associated with generating functions satisfying a composition scheme F(z) = G(H(z)). The analysis becomes challenging when this scheme is critical (i.e., G and H are simultaneously singular). Motivated by many examples (random mappings, planar maps, directed lattice paths), we consider a natural extension of this scheme, namely F(z, u) = G(uH(z))M(z). We also consider a variant of this scheme, which allows us to analyse the number of H-...
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作者：Qin, Qian
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：The theory of two projections is utilized to study two-component Gibbs samplers. Through this theory, previously intractable problems regarding the asymptotic variances of two-component Gibbs samplers are reduced to elementary matrix algebra exercises. It is found that in terms of asymptotic variance, the two-component random-scan Gibbs sampler is never much worse, and could be considerably better than its deterministic-scan counterpart, provided that the selection probability is appropriately...
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作者：Erhard, Dirk; Reis, Guilherme
作者单位：Universidade Federal da Bahia; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We introduce a simple but powerful strategy to study processes driven by two or more reinforcement mechanisms in competition. We apply our method to two types of models: to nonconservative zero range processes on finite graphs, and to multi-particle random walks with positive and negative reinforcement on the edges. The results hold for a broad class of reinforcement functions, including those with superlinear growth. Our strategy consists in a comparison of the original processes with suitabl...
