共查询到20条相似文献,搜索用时 0 毫秒
1.
Xicheng Zhang 《Stochastic Processes and their Applications》2011,121(6):1373-1388
In this article we prove that stochastic differential equation (SDE) with Sobolev drift on a compact Riemannian manifold admits a unique ν-almost everywhere stochastic invertible flow, where ν is the Riemannian measure, which is quasi-invariant with respect to ν. In particular, we extend the well-known DiPerna-Lions flows of ODEs to SDEs on a Riemannian manifold. 相似文献
2.
Xicheng Zhang 《Journal of Differential Equations》2011,250(4):1924-1966
In this article, using DiPerna-Lions theory (DiPerna and Lions, 1989) [1], we investigate linear second order stochastic partial differential equations with unbounded and degenerate non-smooth coefficients, and obtain several conditions for existence and uniqueness. Moreover, we also prove the L1-integrability and a general maximal principle for generalized solutions of SPDEs. As applications, we study nonlinear filtering problem and also obtain the existence and uniqueness of generalized solutions for a degenerate nonlinear SPDE. 相似文献
3.
In this note, we give a short proof for the DiPerna-Lions flows associated to ODEs following the method of Crippa and De Lellis [3]. More precisely, assume that [divb] ∈ Ll∞oc(Rd), |b|/(1 + |x| log |x|) ∈ L∞(Rd) and | b| φ(| b|) ∈ Ll1oc(Rd), where φ(r) = log log(r + c), c > 0. Then, there exists a unique regular Lagrangian flow associated with the ODE X˙(t, x) = b(X(t, x)), X(0, x) = x. 相似文献
4.
We prove the bicontinuity and homeomorphic property of solutions of stochastic differential equations driven by infinite many Brownian motions and with non-Lipschitz coefficients. 相似文献
5.
Jiagang Ren 《Journal of Functional Analysis》2006,241(2):439-456
Let Xt(x) solve the following Itô-type SDE (denoted by EQ.(σ,b,x)) in Rd
6.
Xicheng Zhang 《Journal of Functional Analysis》2010,258(4):1361-1425
In this paper, we study the existence-uniqueness and large deviation estimate for stochastic Volterra integral equations with singular kernels in 2-smooth Banach spaces. Then we apply them to a large class of semilinear stochastic partial differential equations (SPDE), and obtain the existence of unique maximal strong solutions (in the sense of SDE and PDE) under local Lipschitz conditions. Moreover, stochastic Navier-Stokes equations are also investigated. 相似文献
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8.
Guangqiang LAN 《Frontiers of Mathematics in China》2013,8(6):1307-1321
We study the large deviation principle of stochastic differential equations with non-Lipschitzian and non-homogeneous coefficients. We consider at first the large deviation principle when the coefficients σ and b are bounded, then we generalize the conclusion to unbounded case by using bounded approximation program. Our results are generalization of S. Fang-T. Zhang's results. 相似文献
9.
王志明 《数学物理学报(B辑英文版)》2018,38(1):157-168
For a stochastic differential equation with non-Lipschitz coefficients, we construct, by Euler scheme, a measurable flow of the solution, and we prove the solution is a Markov process. 相似文献
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11.
By using finite-dimensional approximations and a recent result on gradient estimates for singular diffusions on Rd, gradient estimates are derived for the semigroups of solutions to a class of stochastic evolution equations on Hilbert spaces with non-Lipschitz coefficients. 相似文献
12.
Boualem Djehiche 《Journal of Mathematical Analysis and Applications》2011,384(1):63-69
In this note, nonlinear stochastic partial differential equations (SPDEs) with continuous coefficients are studied. Via the solutions of backward doubly stochastic differential equations (BDSDEs) with continuous coefficients, we provide an existence result of stochastic viscosity sub- and super-solutions to this class of SPDEs. Under some stronger conditions, we prove the existence of stochastic viscosity solutions. 相似文献
13.
《Stochastic Processes and their Applications》2020,130(5):2639-2674
Given a stochastic differential equation with path-dependent coefficients driven by a multidimensional Wiener process, we show that the support of the law of the solution is given by the image of the Cameron–Martin space under the flow of mild solutions to a system of path-dependent ordinary differential equations. Our result extends the Stroock–Varadhan support theorem for diffusion processes to the case of SDEs with path-dependent coefficients. The proof is based on functional Itô calculus. 相似文献
14.
Hidekazu Yoshioka Koichi Unami Toshihiko Kawachi 《Applied Mathematical Modelling》2012,36(4):1796-1805
A mathematical model of Lagrangian motions of a particle in turbulent flows is developed on the basis of a stochastic differential equation. The model expresses uncertainties involved in turbulence by standard Brownian motion. Because the model does not guarantee smoothness of the path of the particle, local velocity is newly defined so as to be suitable for observation of a velocity time series at a fixed point. Then, it is shown that the newly defined local velocity is governed by a Gaussian distribution. In addition, an estimation method of the turbulent diffusion coefficient involved in the model is proposed by using the local velocity. The estimation method does not require tracer experiments. In order to assess the validity of the proposed local velocity, velocity measurements with three-dimensional acoustic Doppler velocimeters were conducted in agricultural drainage canals. Also, the turbulent diffusion coefficient was estimated by the derived time series of the observed local velocity. Finally, a transport equation of conservative solute is derived by using the linearity of the Kolmogorov forward equation without using gradient-type lows. 相似文献
15.
Guangying Lv 《Applicable analysis》2017,96(16):2737-2757
In this paper, we study the existence and uniqueness of strong solutions for stochastic partial functional differential equations with locally monotone coefficients, locally Lipschitz non-linearity, and time delay. Our results extend previous results obtained by Liu–Röckner, Caraballo et al. and Taniguchi et al. Examples are given to illustrate the wide applicability of our results. 相似文献
16.
We develop an Lp -theory of stochastic PDEs of divergence form. Under natural assumptions on the coefficients and the data, we show that the solutions belong to some modified stochastic Sobolev spaces. As a consequence of this result and certain embedding theorem, we also show that the solutions are Holder continuous in space and time a.s. for sufficiently large p 相似文献
17.
《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(1-2):141-165
An implicit scheme is considered to approximate an abstract Ornstein-Uhlenbeck equation and a 2-dimensional stochastic Navier-Stokes equation with a general white noise. The aim is to prove convergence of solutions, in different acceptions (pathwise, in probability, in distribution), under a corresponding approximation of the noise 相似文献
18.
We consider the Itô stochastic differential equation on Rd. The diffusion coefficients A1,…,Am are supposed to be in the Sobolev space with p>d, and to have linear growth. For the drift coefficient A0, we distinguish two cases: (i) A0 is a continuous vector field whose distributional divergence δ(A0) with respect to the Gaussian measure γd exists, (ii) A0 has Sobolev regularity for some p′>1. Assume for some λ0>0. In case (i), if the pathwise uniqueness of solutions holds, then the push-forward #(Xt)γd admits a density with respect to γd. In particular, if the coefficients are bounded Lipschitz continuous, then Xt leaves the Lebesgue measure Lebd quasi-invariant. In case (ii), we develop a method used by G. Crippa and C. De Lellis for ODE and implemented by X. Zhang for SDE, to establish existence and uniqueness of stochastic flow of maps. 相似文献
19.
Let M be a d-dimensional compact Riemannian manifold. We prove existence of a unique global strong solution of the stochastic wave equation , where Y is a C1-smooth transformation and W is a spatially homogeneous Wiener process on whose spectral measure has finite moments up to order 2. 相似文献
20.
Eduardo Abi Jaber Bruno Bouchard Camille Illand 《Stochastic Processes and their Applications》2019,129(5):1726-1748
This paper provides a new characterization of the stochastic invariance of a closed subset of with respect to a diffusion. We extend the well-known inward pointing Stratonovich drift condition to the case where the diffusion matrix can fail to be differentiable: we only assume that the covariance matrix is. In particular, our result can be applied to construct affine and polynomial diffusions on any arbitrary closed set. 相似文献