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作者：Liang, Gechun; Lyons, Terry; Qian, Zhongmin
作者单位：University of Oxford; University of Oxford
摘要：We demonstrate that backward stochastic differential equations (BSDE) may be reformulated as ordinary functional differential equations on certain path spaces. In this framework, neither Ito's integrals nor martingale representation formulate are needed. This approach provides new tools for the study of BSDE, and is particularly useful for the study of BSDE with partial information. The approach allows us to study the following type of backward stochastic differential equations: dY(t)(j) = -f(...
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作者：Yadin, Ariel; Yehudayoff, Amir
作者单位：University of Cambridge; Technion Israel Institute of Technology
摘要：Lawler, Schramm and Werner showed that the scaling limit of the loop-erased random walk on Z(2) is SLE(2). We consider scaling limits of the loop-erasure of random walks on other planar graphs (graphs embedded into C so that edges do not cross one another). We show that if the scaling limit of the random walk is planar Brownian motion, then the scaling limit of its loop-erasure is SLE(2). Our main contribution is showing that for such graphs, the discrete Poisson kernel can be approximated by ...
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作者：Li, Xue-Mei; Scheutzow, Michael
作者单位：University of Warwick; Technical University of Berlin
摘要：It is well known that a stochastic differential equation (SDE) on a Euclidean space driven by a Brownian motion with Lipschitz coefficients generates a stochastic flow of homeomorphisms. When the coefficients are only locally Lipschitz, then a maximal continuous flow still exists but explosion in finite time may occur. If, in addition, the coefficients grow at most linearly, then this flow has the property that for each fixed initial condition x, the solution exists for all times almost surely...
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作者：Burdzy, Krzysztof; Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：We study Markov processes where the time parameter is replaced by paths in a directed graph from an initial vertex to a terminal one. Along each directed path the process is Markov and has the same distribution as the one along any other directed path. If two directed paths do not interact, in a suitable sense, then the distributions of the processes on the two paths are conditionally independent, given their values at the common endpoint of the two paths. Conditions on graphs that support suc...
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作者：Bordenave, Charles; Caputo, Pietro; Chafai, Djalil
作者单位：Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Roma Tre University; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel
摘要：We consider the random reversible Markov kernel K obtained by assigning i.i.d. nonnegative weights to the edges of the complete graph over n vertices and normalizing by the corresponding row sum. The weights are assumed to be in the domain of attraction of an a-stable law, alpha is an element of (0, 2). When 1 <= alpha < 2, we show that for a suitable regularly varying sequence kappa(n) of index 1 - 1/alpha, the limiting spectral distribution mu(alpha) of kappa(n) K coincides with the one of t...
