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By
Ren, Jiagang; Xu, Siyan; Zhang, Xicheng
15 Citations
We prove a large deviation principle of Freidlin–Wentzell type for multivalued stochastic differential equations with monotone drifts that in particular contain a class of SDEs with reflection in a convex domain.
By
Ren, Jiagang; Röckner, Michael
2 Citations
Abstract.
We prove Höldercontinuity on rays in the direction of vectors in the (generalized) CameronMartin space for functions in Sobolev spaces in L^{p} of fractional order α∈ (
, 1) over infinite dimensional linear spaces. The underlying measures are required to satisfy some easy standard structural assumptions only. Apart from Wiener measure they include Gibbs measures on a lattice and Euclidean interacting quantum fields in infinite volume. A number of applications, e.g., to the twodimensional polymer measure, are presented. In particular, irreducibility of the Dirichlet form associated with the latter measure is proved without restrictions on the coupling constant.
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By
Gao, Fuqing; Ren, Jiagang
8 Citations
Large deviations for stochastic flow solutions to SDEs containing a small parameter are studied. The obtained results are applied to establish a C_{p,r},large deviation principle for stochastic flows and for solutions to anticipating SDEs. The recent results of MilletNualartSans and Yoshida are improved and refined.
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By
Ren, Jiagang; Wu, Jing
This paper deals with the uniform large deviations for multivalued stochastic differential equations (MSDEs for short) by applying a stability result of the viscosity solutions of second order HamiltonJacobiBelleman equations with multivalued operators. Moreover, the large deviation principle is uniform in time and in starting point.
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By
Ren, Jiagang; Shi, Qun; Wu, Jing
1 Citations
We establish various limit theorems for onedimensional stochastic variational inequalities with YamadaWatanabe type conditions on the coefficients, including, the construction of the solution through the Euler scheme, the convergence of the Yosida approximation and stability of the solution. Besides, convergence rates are presented for these two approximations when the coefficients are only Hölder continuous.
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By
Ren, Jiagang; Wu, Jing; Zhang, Hua
5 Citations
In this paper, we prove a large deviation principle of Freidlin–Wentzell type for multivalued stochastic differential equations (MSDEs) that is a little more general than the results obatined by Ren et al. (J Theor Prob 23:1142–1156, 2010). As an application, we derive a functional iterated logarithm law for the solutions of MSDEs.
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By
Ren, Jiagang; Röckner, Michael; Zhang, Xicheng
1 Citations
In this paper, we first extend the classical Itô stochastic integral to the case of measurable fields of Hilbert spaces. Then, a Kusuoka–Stroock formula on configuration space is proved. Using this formula, we study the fractional regularities of local times with jumps in the sense of the Malliavin calculus.
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By
Ren, Jiagang; Wu, Jing
We prove the existence and uniqueness of solutions of multivalued stochastic differential equations driven by Poisson point processes when the domain of the multivalued maximal monotone operator is the whole space Rd.
By
Ren, Jiagang; Zhang, Hua
In this paper, we study the regularity of the laws of stochastic differential equations with jumps using the recently welldeveloped lent particle method introduced by Bouleau and Denis under some kind of Hörmander’s conditions.
