19 Citations
Local Invertibility of Adapted Shifts on Wiener Space and Related Topics
- Mathematics
- 2013
In this article we show that the invertibility of an adapted shift on the Brownian sheet is a local property in the usual sense of stochastic calculus. Thanks to this result we give a short proof of…
Variational Calculation of Laplace transforms via Entropy on Wiener Space and some Applications
- Mathematics
- 2014
Parametric Regularity of the Conditional Expectations via the Malliavin Calculus and Applications
- Mathematics
- 2013
Let (W, H, μ) be the classical Wiener space and assume that \(U_{\lambda } = I_{W} + u_{\lambda }\) is an adapted perturbation of identity where the perturbation u λ is an H-valued map, defined up to…
Variational calculus on Wiener space with respect to conditional expectations
- Mathematics
- 2016
We give a variational formulation for $-\log\mathbb{E}_\nu\left[e^{-f}|\mathcal{F}_t\right]$ for a large class of measures $\nu$. We give a refined entropic characterization of the invertibility of…
Local invertibility of adapted shifts on Wiener space, under finite energy condition
- Mathematics
- 2013
In this paper we study the connection between local invertibility and global invertibility of adapted shifts on Wiener space. First we go from the global to the local and we obtain an explicit…
A general framework for variational calculus on Wiener space
- Mathematics
- 2016
We provide a framework to derive a variational formulation for $-\log\mathbb{E}_\nu\left[e^{-f}\right]$ for a large class of measures $\nu$. We use a family of perturbations of the identity $(W^u)$…
A comparison theorem for stochastic differential equations under a Novikov-type condition
- Mathematics
- 2013
We consider a system of stochastic differential equations driven by a standard n-dimensional Brownian motion where the drift coefficient satisfies a Novikov-type condition while the diffusion…
Martingale representation for degenerate diffusions
- MathematicsJournal of Functional Analysis
- 2019
On the form of the relative entropy between measures on the space of continuous functions
- Mathematics
- 2013
In this paper we derive an integral (with respect to time) representation of the relative entropy (or Kullback-Leibler Divergence) between measures mu and P on the space of continuous functions from…
References
SHOWING 1-10 OF 17 REFERENCES
Sufficient conditions for the invertibility of adapted perturbations of identity on the Wiener space
- Mathematics
- 2006
Let (W, H, μ) be the classical Wiener space. Assume that U = IW + u is an adapted perturbation of identity, i.e., u : W → H is adapted to the canonical filtration of W. We give some sufficient…
The realization of positive random variables via absolutely continuous transformations of measure on Wiener space
- Mathematics
- 2006
Let $\mu$ be a Gaussian measure on some measurable space $\{W=\{w\},{\mathcal{B}}(W)\}$ and let $\nu$ be a measure on the same space which is absolutely continuous with respect to $\nu$. The paper…
Monge-Kantorovitch Measure Transportation and Monge-Ampère Equation on Wiener Space
- Mathematics
- 2004
AbstractLet (W,μ,H) be an abstract Wiener space assume two νi,i=1,2 probabilities on (W,ℬ(W)). We give some conditions for the Wasserstein distance between ν1 and ν2 with respect to the…
Transformation of Measure on Wiener Space
- Mathematics
- 2000
This book gives a systematic presentation of the main results on the transformation of measure induced by shift transformations on Wiener space. This topic has its origins in the work of Cameron and…
A variational representation for certain functionals of Brownian motion
- Mathematics
- 1998
In this paper we show that the variational representation - log Ee -f(W) = inf E{1/2∫ 0 1 ∥v s ∥ 2 ds + f(w + ∫ 0 v s ds)} holds, where W is a standard d-dimensional Brownian motion, f is any bounded…
Transportation cost for Gaussian and other product measures
- Mathematics
- 1996
AbstractConsider the canonical Gaussian measure γN on ℝ, a probability measure μ on ℝN, absolutely continuous with respect to γN. We prove that the transportation cost of μ to γN, when the cost of…
An Introduction to Analysis on Wiener Space
- Mathematics
- 1995
Preliminaries.- Gross-Sobolev derivative, divergence and Ornstein-Uhlenbeck operator.- Meyer inequalities.- Hypercontractivity.- L p -multipliers theorem, meyer inequalities and distributions.- Some…
The Notion of Convexity and Concavity on Wiener Space
- Mathematics
- 2000
Abstract We define, in the frame of an abstract Wiener space, the notions of convexity and of concavity for the equivalence classes of random variables. As application we show that some important…
Stochastic differential equations for the non linear filtering problem
- Mathematics
- 1972
The general nonlinear filtering or estimation problem may be described as follows. xty (0<t<T)y called the signal or system process is a stochastic process direct observation is not possible. The…
Analysis on Wiener Space and Applications
- Mathematics
- 2010
The aim of this book is to give a rigorous introduction for the graduate students to Analysis on Wiener space, a subject which has grown up very quickly these recent years under the new impulse of…