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作者：Giles, Michael b.; Aji-ali, Abdul-lateef
作者单位：University of Oxford; Heriot Watt University; University of Edinburgh
摘要：We propose a new Monte Carlo-based estimator for digital options with assets modelled by a stochastic differential equation (SDE). The new estimator is based on repeated path splitting and relies on the correlation of approximate paths of the underlying SDE that share parts of a Brownian path. Combining this new estimator with multilevel Monte Carlo (MLMC) leads to an estimator with a computational complexity that is similar to the complexity of a MLMC estimator when applied to options with Li...
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作者：Kardaras, Constantinos
作者单位：University of London; London School Economics & Political Science
摘要：Stochastic integrals are defined with respect to a collection P = (P-i; i is an element of I) of continuous semimartingales, imposing no assumptions on the index set I and the subspace of R-I where P takes values. The integrals are constructed though finite-dimensional approximation, identifying the appropriate local geometry that allows extension to infinite dimensions. For local martingale integrators, the resulting space S(P) of stochastic integrals has an operational characterisation via a...
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作者：Goldfeld, Ziv; Kato, Kengo; Nietert, Sloan; Rioux, Gabriel
作者单位：Cornell University; Cornell University; Cornell University; Cornell University
摘要：The Wasserstein distance is a metric on a space of probability measures that has seen a surge of applications in statistics, machine learning, and applied mathematics. However, statistical aspects of Wasserstein distances are bottlenecked by the curse of dimensionality, whereby the number of data points needed to accurately estimate them grows exponentially with dimension. Gaussian smoothing was recently introduced as a means to alleviate the curse of dimensionality, giving rise to a parametri...
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作者：Jourdain, Benjamin; Menozzi, Stephane
作者单位：Inria; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite Paris Saclay
摘要：We are interested in the time discretization of stochastic differential equations with additive d-dimensional Brownian noise and L-q - L-rho drift coefficient when the condition d/rho + 2/q < 1, under which Krylov and Rockner (Probab. Theory Related Fields 131 (2005) 154-196) proved existence of a unique strong solution, is met. We show weak convergence with order 1/2 (1 - (d/rho + 2/q)) which corresponds to half the distance to the threshold for the Euler scheme with randomized time variable ...
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作者：Bhattacharya, Sohom; Deb, Nabarun; Mukherjee, Sumit
作者单位：State University System of Florida; University of Florida; University of Chicago; Columbia University
摘要：In this paper we derive a large deviation principle (LDP) for inhomogeneous U/V-statistics of a general order. Using this, we derive a LDP for two types of statistics: random multilinear forms, and number of monochromatic copies of a subgraph. We show that the corresponding rate functions in these cases can be expressed as a variational problem over a suitable space of functions. We use the tools developed to study Gibbs measures with the corresponding Hamiltonians, which include tensor genera...
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作者：Alon, Noga; Elboim, Dor; Sly, Allan
作者单位：Princeton University
摘要：Georgiou, Katkov and Tsodyks considered the following random process. Let x(1), x(2), . . . be an infinite sequence of independent, identically distributed, uniform random points in [0, 1]. Starting with S = {0}, the elements x(k) join S one by one, in order. When an entering element is larger than the current minimum element of S, this minimum leaves S. Let S(1, n) denote the content of S after the first n elements x(k) join. Simulations suggest that the size |S(1, n)| of S at time n is typic...
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作者：Jackson, Joe
作者单位：University of Texas System; University of Texas Austin
摘要：Using probabilistic methods, we establish a priori estimates for two classes of quasilinear parabolic systems of partial differential equations (PDEs). We treat in particular the case of a nonlinearity, which has quadratic growth in the gradient of the unknown. As a result of our estimates, we obtain the existence of classical solutions of the PDE system. From this, we infer the existence of solutions to a corresponding class of forward backward stochastic differential equations.
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作者：Han, Fang; Huang, Zhihan
作者单位：University of Washington; University of Washington Seattle; University of Pennsylvania
摘要：In their seminal work, Azadkia and Chatterjee ( Ann. Statist. 49 (2021) 3070-3102) initiated graph-based methods for measuring variable dependence strength. By appealing to nearest neighbor graphs based on the Euclidean metric, they gave an elegant solution to a problem of R & eacute;nyi ( Acta Math. Acad. Sci. Hung. 10 (1959) 441-451). This idea was later developed in Deb, Ghosal and Sen (2020) (https://arxiv.org/abs/2010.01768) and the authors there proved that, quite interestingly, Azadkia ...
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作者：Alon, Noga; Gunby, Benjamin; He, Xiaoyu; Shmaya, Eran; Solan, Eilon
作者单位：Princeton University; Rutgers University System; Rutgers University New Brunswick; State University of New York (SUNY) System; Stony Brook University; Tel Aviv University
摘要：A group of players are supposed to follow a prescribed profile of strategies. If they follow this profile, they will reach a given target. We show that if the target is not reached because some player deviates, then an outside observer can identify the deviator. We also construct identification methods in two nontrivial cases.
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作者：Deb, Nabarun; Mukherjee, Rajarshi; Mukherjee, Sumit; Yuan, Ming
作者单位：Columbia University; Harvard University
摘要：In this paper we study the effect of dependence on detecting a class of signals in Ising models, where the signals are present in a structured way. Examples include Ising models on lattices, and mean-field type Ising models (Erdos-Renyi, Random regular, and dense graphs). Our results rely on correlation decay and mixing type behavior for Ising models, and demonstrate the beneficial behavior of criticality in detection of strictly lower signals. As a by-product of our proof technique, we develo...
