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1.
Let be a real-valued fractional Brownian sheet. Consider the (N, d) Gaussian random field B
H
defined by
where are independent copies of B
0
H
. In this paper, the existence and joint continuity of the local times of B
H
are established.
Received: 2 October 2001 / Revised version: 7 January 2002 / Published online: 22 August 2002 相似文献
2.
In this paper, we obtain the Varadhan type small time asymptotics for diffusion processes on path groups. 相似文献
3.
Potential Analysis - In this paper, we establish the Freidlin-Wentzell’s large deviations for quasilinear parabolic stochastic partial differential equations with multiplicative noise, which... 相似文献
4.
Olivier Menoukeu-Pamen Thilo Meyer-Brandis Torstein Nilssen Frank Proske Tusheng Zhang 《Mathematische Annalen》2013,357(2):761-799
In this article we develop a new approach to construct solutions of stochastic equations with merely measurable drift coefficients. We aim at demonstrating the principles of our technique by analyzing strong solutions of stochastic differential equations driven by Brownian motion. An important and rather surprising consequence of our method which is based on Malliavin calculus is that the solutions derived by Veretennikov (Theory Probab Appl 24:354–366, 1979) for Brownian motion with bounded and measurable drift in $\mathbb{R }^{d}$ are Malliavin differentiable. Further, a strength of our approach, which does not rely on a pathwise uniqueness argument, is that it can be transferred and applied to the analysis of various other types of (stochastic) equations: We obtain a Bismut–Elworthy–Li formula (Elworthy and Li, J Funct Anal 125:252–286, 1994) for spatial derivatives of solutions to the Kolmogorov equation with bounded and measurable drift coefficients. To derive the formula, we use that our approach can be applied to obtain Sobolev differentiability in the initial condition in addition to Malliavin differentiability of the associated stochastic differential equations. Another application of our technique is the construction of unique solutions of the stochastic transport equation with irregular vector fields. Moreover, our approach is also applicable to the construction of solutions of stochastic evolution equations on Hilbert spaces. 相似文献
5.
In this article, we develop a large deviation principle (LDP) for a class of retarded Ornstein-Uhlenbeck processes driven by Lévy processes. We first present a LDP result for time delay systems driven by cylindrical Wiener processes based on the large deviations of Gaussian processes. By using a contraction technique and passing on a finite-dimensional approximation, an LDP is obtained for stochastic time delay evolution equations driven by additive Lévy noise, whose solutions are generally not Lévy processes any more. 相似文献
6.
A non-negative Markovian solution is constructed for a class of stochastic generalized porous media equations with reflection. To this end, some regularity properties and a comparison theorem are proved for stochastic generalized porous media equations, which are interesting by themselves. Invariant probability measures and ergodicity of the solution are also investigated. 相似文献
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8.
Tusheng Zhang 《Stochastic Processes and their Applications》2012,122(10):3425-3444
In this article, we establish a large deviation principle for invariant measures of solutions of stochastic partial differential equations with two reflecting walls driven by a space–time white noise. 相似文献
9.
A new result for the pathwise uniqueness of solutions of stochastic differential equations with non-Lipschitzian coefficients is established. Furthermore, we prove that the solution has no explosion under the growth ξlogξ. To cite this article: S. Fang, T. Zhang, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
10.
In this paper, we obtain a characterization of invariant measures of stochastic evolution equations and stochastic partial differential equations of pure jump type. As an application, it is shown that the equation has a unique invariant probability measure under some reasonable conditions. 相似文献