Search results for "Malliavin Calculus"
showing 10 items of 21 documents
A Criterium for the Strict Positivity of the Density of the Law of a Poisson Process
2011
We translate in semigroup theory our result (Leandre, 1990) giving a necessary condition so that the law of a Markov process with jumps could have a strictly positive density. This result express, that we have to jump in a finite number of jumps in a "submersive" way from the starting point to the end point if the density of the jump process is strictly positive in . We use the Malliavin Calculus of Bismut type of (Leandre, (2008;2010)) translated in semi-group theory as a tool, and the interpretation in semi-group theory of some classical results of the stochastic analysis for Poisson process as, for instance, the formula giving the law of a compound Poisson process.
Regularity of a Degenerated Convolution Semi-Group Without to Use the Poisson Process
2011
We translate in semi-group theory our regularity result for a degenerated convolution semi-group got by the Malliavin Calculus of Bismut type for Poisson processes.
Bismut’s Way of the Malliavin Calculus for Non-Markovian Semi-groups: An Introduction
2019
We give a review of our recent works related to the Malliavin calculus of Bismut type for non-Markovian generators. Part IV is new and relates the Malliavin calculus and the general theory of elliptic pseudo-differential operators.
The interrelation between stochastic differential inclusions and set-valued stochastic differential equations
2013
Abstract In this paper we connect the well established theory of stochastic differential inclusions with a new theory of set-valued stochastic differential equations. Solutions to the latter equations are understood as continuous mappings taking on their values in the hyperspace of nonempty, bounded, convex and closed subsets of the space L 2 consisting of square integrable random vectors. We show that for the solution X to a set-valued stochastic differential equation corresponding to a stochastic differential inclusion, there exists a solution x for this inclusion that is a ‖ ⋅ ‖ L 2 -continuous selection of X . This result enables us to draw inferences about the reachable sets of solutio…
Varadhan estimates without probability: lower bound
2007
We translate in semi-group theory our proof of Varadhan estimates for subelliptic Laplacians which was using the theory of large deviations of Wentzel-Freidlin and the Malliavin Calculus of Bismut type.
Malliavin Calculus and Skorohod Integration for Quantum Stochastic Processes
2000
A derivation operator and a divergence operator are defined on the algebra of bounded operators on the symmetric Fock space over the complexification of a real Hilbert space $\eufrak{h}$ and it is shown that they satisfy similar properties as the derivation and divergence operator on the Wiener space over $\eufrak{h}$. The derivation operator is then used to give sufficient conditions for the existence of smooth Wigner densities for pairs of operators satisfying the canonical commutation relations. For $\eufrak{h}=L^2(\mathbb{R}_+)$, the divergence operator is shown to coincide with the Hudson-Parthasarathy quantum stochastic integral for adapted integrable processes and with the non-causal…
Stochastic Differential Calculus
1993
In many cases of engineering interest it has become quite common to use stochastic processes to model loadings resulting from earthquake, turbulent winds or ocean waves. In these circumstances the structural response needs to be adequately described in a probabilistic sense, by evaluating the cumulants or the moments of any order of the response (see e.g. [1, 2]). In particular, for linear systems excited by normal input, the response process is normal too and the moments or the cumulants up to the second order fully characterize the probability density function of both input and output processes. Many practical problems involve processes which are approximately normal and the effect of the…
SOME RELATIONS BETWEEN BOUNDED BELOW ELLIPTIC OPERATORS AND STOCHASTIC ANALYSIS
2019
International audience; We apply Malliavin Calculus tools to the case of a bounded below elliptic rightinvariant Pseudodifferential operators on a Lie group. We give examples of bounded below pseudodifferential elliptic operators on R d by using the theory of Poisson process and the Garding inequality. In the two cases, there is no stochastic processes besides because the considered semi-groups do not preserve positivity.
Bismut's Way of the Malliavin Calculus for Elliptic Pseudodifferential Operators on a Lie Group
2018
We give an adaptation of the Malliavin Calculus of Bismut type for a semi-group generated by a right-invariant elliptic pseudodifferential operator on a Lie group.
Ambit processes and stochastic partial differential equations
2011
Ambit processes are general stochastic processes based on stochastic integrals with respect to Levy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection between ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Levy noise analysis.