共查询到20条相似文献,搜索用时 46 毫秒
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Christian Bender Peter Parczewski 《Stochastic Processes and their Applications》2018,128(8):2489-2537
Suppose is a Brownian motion and is an approximating sequence of rescaled random walks on the same probability space converging to pointwise in probability. We provide necessary and sufficient conditions for weak and strong -convergence of a discretized Malliavin derivative, a discrete Skorokhod integral, and discrete analogues of the Clark–Ocone derivative to their continuous counterparts. Moreover, given a sequence of random variables which admit a chaos decomposition in terms of discrete multiple Wiener integrals with respect to , we derive necessary and sufficient conditions for strong -convergence to a -measurable random variable via convergence of the discrete chaos coefficients of to the continuous chaos coefficients. 相似文献
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This paper introduces a stochastic scheduling problem. In this problem a directed acyclic graphs (DAG) represents the precedence relations among tasks that workers are scheduled to execute. The question is to find a schedule such that if tasks are assigned to workers according to , the expected time needed to execute all the tasks is minimized. The time needed to execute task by worker is a random variable expressed by a negative exponential distribution with parameter and each task can be executed by more than one worker at a time. In this paper, we will prove that the problem in its general form is NP-hard, but when the DAG width is constant, we will show that the optimum schedules can be found in polynomial time. 相似文献
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This paper develops systematically the stochastic calculus via regularization in the case of jump processes. In particular one continues the analysis of real-valued càdlàg weak Dirichlet processes with respect to a given filtration. Such a process is the sum of a local martingale and an adapted process such that , for any continuous local martingale . Given a function , which is of class (or sometimes less), we provide a chain rule type expansion for which stands in applications for a chain Itô type rule. 相似文献
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Simone Franchini 《Stochastic Processes and their Applications》2017,127(10):3372-3411
We consider a generalized two-color Polya urn (black and white balls) first introduced by Hill et al. (1980), where the urn composition evolves as follows: let , and denote by the fraction of black balls after step , then at step a black ball is added with probability and a white ball is added with probability . Originally introduced to mimic attachment under imperfect information, this model has found applications in many fields, ranging from Market Share modeling to polymer physics and biology.In this work we discuss large deviations for a wide class of continuous urn functions . In particular, we prove that this process satisfies a Sample-Path Large Deviations principle, also providing a variational representation for the rate function. Then, we derive a variational representation for the limit where is the number of black balls at time , and use it to give some insight on the shape of . Under suitable assumptions on we are able to identify the optimal trajectory. We also find a non-linear Cauchy problem for the Cumulant Generating Function and provide an explicit analysis for some selected examples. In particular we discuss the linear case, which embeds the Bagchi–Pal Model [6], giving the exact implicit expression for in terms of the Cumulant Generating Function. 相似文献
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Ibrahim Ekren 《Stochastic Processes and their Applications》2017,127(12):3966-3996
In this article, we adapt the definition of viscosity solutions to the obstacle problem for fully nonlinear path-dependent PDEs with data uniformly continuous in , and generator Lipschitz continuous in . We prove that our definition of viscosity solutions is consistent with the classical solutions, and satisfy a stability result. We show that the value functional defined via the second order reflected backward stochastic differential equation is the unique viscosity solution of the variational inequalities. 相似文献
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For a highly beneficial mutant entering a randomly reproducing population of constant size, we study the situation when a second beneficial mutant arises before has fixed. If the selection coefficient of is greater than the selection coefficient of , and if and can recombine at some rate , there is a chance that the double beneficial mutant forms and eventually fixes. We give a convergence result for the fixation probability of and its fixation time for large selection coefficients. 相似文献
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Ercan Sönmez 《Stochastic Processes and their Applications》2018,128(2):426-444
Let be a multivariate operator-self-similar random field with values in . Such fields were introduced in [22] and satisfy the scaling property for all , where is a real matrix and is an real matrix. We solve an open problem in [22] by calculating the Hausdorff dimension of the range and graph of a trajectory over the unit cube in the Gaussian case. In particular, we enlighten the property that the Hausdorff dimension is determined by the real parts of the eigenvalues of and as well as the multiplicity of the eigenvalues of and . 相似文献
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A second order asymptotic expansion in the local limit theorem for a simple branching random walk in
Zhi-Qiang Gao 《Stochastic Processes and their Applications》2018,128(12):4000-4017
Consider a branching random walk, where the underlying branching mechanism is governed by a Galton–Watson process and the migration of particles by a simple random walk in . Denote by the number of particles of generation located at site . We give the second order asymptotic expansion for . The higher order expansion can be derived by using our method here. As a by-product, we give the second order expansion for a simple random walk on , which is used in the proof of the main theorem and is of independent interest. 相似文献
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Adrien Brandejsky Benoîte de Saporta François Dufour 《Stochastic Processes and their Applications》2013
This paper deals with the optimal stopping problem under partial observation for piecewise-deterministic Markov processes. We first obtain a recursive formulation of the optimal filter process and derive the dynamic programming equation of the partially observed optimal stopping problem. Then, we propose a numerical method, based on the quantization of the discrete-time filter process and the inter-jump times, to approximate the value function and to compute an ?-optimal stopping time. We prove the convergence of the algorithms and bound the rates of convergence. 相似文献
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We consider a -dimensional random field that solves a system of elliptic stochastic equations on a bounded domain , with additive white noise and spatial dimension . Properties of and its probability law are proved. For Gaussian solutions, using results from Dalang and Sanz-Solé (2009), we establish upper and lower bounds on hitting probabilities in terms of the Hausdorff measure and Bessel–Riesz capacity, respectively. This relies on precise estimates of the canonical distance of the process or, equivalently, on estimates of increments of the Green function of the Laplace equation. 相似文献
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This paper considers the martingale problem for a class of weakly coupled Lévy type operators. It is shown that under some mild conditions, the martingale problem is well-posed and uniquely determines a strong Markov process . The process , called a regime-switching jump diffusion with Lévy type jumps, is further shown to possess Feller and strong Feller properties under non-Lipschitz conditions via the coupling method. 相似文献
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Christophe Gallesco Sandro Gallo Daniel Y. Takahashi 《Stochastic Processes and their Applications》2018,128(2):689-706
We say that a probability kernel exhibits dynamic uniqueness (DU) if all the stochastic chains starting from a fixed past coincide on the future tail -algebra. Our first theorem is a set of properties that are pairwise equivalent to DU which allow us to understand how it compares to other more classical concepts. In particular, we prove that DU is equivalent to a weak- summability condition on the kernel. As a corollary to this theorem, we prove that the Bramson–Kalikow and the long-range Ising models both exhibit DU if and only if their kernels are summable. Finally, if we weaken the condition for DU, asking for coincidence on the future -algebra for almost every pair of pasts, we obtain a condition that is equivalent to -mixing (weak-Bernoullicity) of the compatible stationary chain. As a consequence, we show that a modification of the weak- summability condition on the kernel is equivalent to the -mixing of the compatible stationary chain. 相似文献
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Ekaterina Vl. Bulinskaya 《Stochastic Processes and their Applications》2018,128(7):2325-2340
For a supercritical catalytic branching random walk on , , with an arbitrary finite catalysts set we study the spread of particles population as time grows to infinity. It is shown that in the result of the proper normalization of the particles positions in the limit there are a.s. no particles outside the closed convex surface in which we call the propagation front and, under condition of infinite number of visits of the catalysts set, a.s. there exist particles on the propagation front. We also demonstrate that the propagation front is asymptotically densely populated and derive its alternative representation. 相似文献