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## Large Deviations for Multivalued Stochastic Differential Equations

### Journal of Theoretical Probability (2010-12-01) 23: 1142-1156 , December 01, 2010

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.

## Ray Hölder-continuity for fractional Sobolev spaces in infinite dimensions and applications

### Probability Theory and Related Fields (2000-06-01) 117: 201-220 , June 01, 2000

### Abstract.

We prove Hölder-continuity on rays in the direction of vectors in the (generalized) Cameron-Martin 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 two-dimensional polymer measure, are presented. In particular, irreducibility of the Dirichlet form associated with the latter measure is proved without restrictions on the coupling constant.

## Large deviations for stochastic flows and their applications

### Science in China Series A: Mathematics (2001-08-01) 44: 1016-1033 , August 01, 2001

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 Millet-Nualart-Sans and Yoshida are improved and refined.

## General Large Deviations and Functional Iterated Logarithm Law for Multivalued Stochastic Differential Equations

### Journal of Theoretical Probability (2015-06-01) 28: 550-586 , June 01, 2015

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.

## Kusuoka–Stroock Formula on Configuration Space and Regularities of Local Times with Jumps

### Potential Analysis (2007-06-01) 26: 363-396 , June 01, 2007

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.

## Multi-valued Stochastic Differential Equations Driven by Poisson Point Processes

### Stochastic Analysis with Financial Applications (2011-01-01) 65: 191-205 , January 01, 2011

We prove the existence and uniqueness of solutions of multi-valued stochastic differential equations driven by Poisson point processes when the domain of the multi-valued maximal monotone operator is the whole space Rd.