共查询到20条相似文献,搜索用时 15 毫秒
1.
Denis Bell 《Journal of Functional Analysis》2007,251(1):232-253
Let x denote a diffusion process defined on a closed compact manifold. In an earlier article, the author introduced a new approach to constructing admissible vector fields on the associated space of paths, under the assumption of ellipticity of x. In this article, this method is extended to yield similar results for degenerate diffusion processes. In particular, these results apply to non-elliptic diffusions satisfying Hörmander's condition. 相似文献
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3.
Shizan Fang 《Bulletin des Sciences Mathématiques》2005,129(4):339-355
The gradient operator is defined on the free path space with reference measure Pμ, the law of the Brownian motion on the base manifold with initial distribution μ, where μ has strictly positive density w.r.t. the volume measure. The formula of integration by parts is established for the underlying directional derivatives, which implies the closability of the gradient operator so that it induces a conservative Dirichlet form on the free path space. The log-Sobolev inequality for this Dirichlet form is established and, consequently, the transportation cost inequality is obtained for the associated intrinsic distance. 相似文献
4.
谢鹏 《数学物理学报(B辑英文版)》2005,25(4):639-646
1IntroductionA limit theorem for the approximation of solutions of stochastic di?erential equations bythose of ordinary di?erential equations was first established by Stroock and Varadhan[8]andits various versions were studied e.g.in[1],[5],[6].They have … 相似文献
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In this paper, we construct a finite dimensional approximation for the geometry on the path space over a compact Riemannian manifold. This approximation allows to construct the horizontal lift of the Ornstein-Uhlenbeck process on the path space through the Markovian connection. We also prove a representation formula for the heat semigroup on (adapted) vector fields as well as a commutation formula for its derivative. 相似文献
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In this paper,we prove that the generator g of a class of backward stochastic differential equations (BSDEs) can be represented by the solutions of the corresponding BSDEs at point (t,y,z),when the terminal data is in L p spaces,for 1 < p ≤ 2. 相似文献
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We study comparison theorems for one dimensional anticipated backward stochastic differential equations under one kind of non-Lipschitz assumption. In the results, the generator functions are allowed to contain the anticipated term of z, neither generator function needs to be necessarily monotone in the anticipated term of y , and the anticipated times of the anticipated terms of (y,z) in one generator function can differ from those in the other. 相似文献
8.
Shaoqin ZHANG 《Frontiers of Mathematics in China》2016,11(2):461-496
Shift Harnack inequality and integration by parts formula are established for semilinear stochastic partial differential equations and stochastic functional partial differential equations by modifying the coupling used by F.-Y. Wang [Ann. Probab., 2012, 42(3): 994–1019]. Log-Harnack inequality is established for a class of stochastic evolution equations with non-Lipschitz coefficients which includes hyperdissipative Navier-Stokes/Burgers equations as examples. The integration by parts formula is extended to the path space of stochastic functional partial differential equations, then a Dirichlet form is defined and the log-Sobolev inequality is established. 相似文献
9.
B. Krishna Das J. Martin Lindsay Orawan Tripak 《Journal of Mathematical Analysis and Applications》2014
A theory of quantum stochastic processes in Banach space is initiated. The processes considered here consist of Banach space valued sesquilinear maps. We establish an existence and uniqueness theorem for quantum stochastic differential equations in Banach modules, show that solutions in unital Banach algebras yield stochastic cocycles, give sufficient conditions for a stochastic cocycle to satisfy such an equation, and prove a stochastic Lie–Trotter product formula. The theory is used to extend, unify and refine standard quantum stochastic analysis through different choices of Banach space, of which there are three paradigm classes: spaces of bounded Hilbert space operators, operator mapping spaces and duals of operator space coalgebras. Our results provide the basis for a general theory of quantum stochastic processes in operator spaces, of which Lévy processes on compact quantum groups is a special case. 相似文献
10.
Stefano Bonaccorsi Lorenzo Zambotti 《Proceedings of the American Mathematical Society》2004,132(3):875-883
We prove infinite-dimensional integration by parts formulae for the laws of the Brownian Meander, of the Bessel Bridge of dimension 3 between and of the Brownian Motion on the set of all paths taking values greater than or equal to a nonpositive constant. We give applications to SPDEs with reflection.
11.
Jeong Hyun Lee 《Proceedings of the American Mathematical Society》2005,133(7):2147-2155
In this paper, we define, motivated by recent works of Chang and Skoug, stochastic integrals for a generalized Brownian motion ( ) and then use it to study the representation problem on the linear space spanned by . We next establish a translation theorem for -functionals of , , and then use this translation to establish an integration by parts formula for -functionals of .
12.
We study nonlinear elliptic SPDEs driven by a space-time white noise. We present existence and uniqueness results for a drift of monotone type and we study the germ Markov property of the solution 相似文献
13.
Xiliang Fan 《随机分析与应用》2015,33(2):199-212
By using coupling by change of measures, the Driver-type integration by parts formula is established for a class of stochastic differential equations driven by fractional Brownian motions. As applications, (log) shift Harnack inequalities and estimates on the distribution density of the solutions are presented. 相似文献
14.
《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(1-2):107-114
Under regularity conditions, a finite dimensional filter system exists for a partially observable process if and only if the conditional distributions involved each form an exponential family of distributions. The filter equation can be derived directly from the exponential representations of these families. 相似文献
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We present a Cameron–Martin type quasi-invariance theorem for subordinate Brownian motion. As applications, we establish an integration by parts formula and construct a gradient operator on the path space of subordinate Brownian motion, and obtain some canonical Dirichlet forms. These findings extend the corresponding classical results for Brownian motion. 相似文献
16.
A class of diffusion processes on the path space over a compact Riemannian manifold is constructed. The diffusion of such a process is governed by an unbounded operator. A representation of the associated generator is derived and the existence of a certain local second moment is shown.
17.
We give some multidimensional Tauberian theorems for generalized functions and show examples of their application in mathematical physics. In particular, we consider the problems of stabilizing the solutions of the Cauchy problem for the heat kernel equation, multicomponent gas diffusion, and the asymptotic Cauchy problem for a free Schrödinger equation in the norms of different Banach spaces among others. 相似文献
18.
A. Kohatsu-Higa D. Márquez-Carreras M. Sanz-Solé 《Journal of Theoretical Probability》2001,14(2):427-462
Consider the density of the solution X(t, x) of a stochastic heat equation with small noise at a fixed t[0, T], x[0, 1]. In this paper we study the asymptotics of this density as the noise vanishes. A kind of Taylor expansion in powers of the noise parameter is obtained. The coefficients and the residue of the expansion are explicitly calculated. In order to obtain this result some type of exponential estimates of tail probabilities of the difference between the approximating process and the limit one is proved. Also a suitable iterative local integration by parts formula is developed. 相似文献
19.
Xiliang FAN 《Frontiers of Mathematics in China》2015,10(3):595
This paper is devoted to study a class of stochastic Volterra equations driven by fractional Brownian motion. We first prove the Driver type integration by parts formula and the shift Harnack type inequalities. As a direct application, we provide an alternative method to describe the regularities of the law of the solution. Secondly, by using the Malliavin calculus, the Bismut type derivative formula is established, which is then applied to the study of the gradient estimate and the strong Feller property. Finally, we establish the Talagrand type transportation cost inequalities for the law of the solution on the path space with respect to both the uniform metric and the L2-metric. 相似文献