• Corpus ID: 118944492

# On existence and properties of strong solutions of one-dimensional stochastic equations with an additive noise

@article{Pilipenko2013OnEA,
title={On existence and properties of strong solutions of one-dimensional stochastic equations with an additive noise},
author={Andrey Pilipenko},
journal={arXiv: Probability},
year={2013}
}
• A. Pilipenko
• Published 2 June 2013
• Mathematics
• arXiv: Probability
One-dimensional stochastic differential equations with additive L\'evy noise are considered. Conditions for existence and uniqueness of a strong solution are obtained. In particular, if the noise is a L\'evy symmetric stable process with $\alpha\in(1;2)$, then the measurability and boundedness of a drift term is sufficient for the existence of a strong solution. We also study continuous dependence of the strong solution on the initial value and the drift.
6 Citations
On existence of strong solutions to stochastic equations with Lévy noise and differentiability with respect to initial condition
• Mathematics
• 2016
is a finite sum and always exists. So there will be no other restrictions on b2 (moreover, the general case reduces to that of b2 = 0), but the conditions on other coefficients are important and will
A comparison theorem for stochastic differential equations under a Novikov-type condition
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
On differentiability with respect to the initial data of the solution to an SDE with a Lévy noise and discontinuous coefficients
• Mathematics
• 2014
We construct a stochastic flow generated by an stochastic differential equation with its drift being a function of bounded variation and its noise being a stable process with exponent from (1,2). It
A Comparison Theorem for Stochastic Differential Equations Under the Novikov Condition
We consider a system of stochastic differential equations driven by a standard n-dimensional Brownian motion where the drift function b is bounded and the diffusion coefficient is the identity
Asymptotic behavior for a time-inhomogeneous stochastic differential equation driven by an α-stable Lévy process
We study a one-dimensional kinetic stochastic model driven by a Lévy process, with a nonlinear time-inhomogeneous drift. More precisely, the process (V,X) is considered, where X is the position of
Kinetic time-inhomogeneous L{\'e}vy-driven model
• Mathematics
• 2021
: We study a one-dimensional kinetic stochastic model driven by a Lévy process with a non-linear time-inhomogeneous drift. More precisely, the process ( V, X ) is considered, where X is the position

## References

SHOWING 1-6 OF 6 REFERENCES
Nonlinear Transformations of Smooth Measures on Infinite-Dimensional Spaces
• Mathematics
• 2000
We investigate the properties of the image of a differentiable measure on an infinitely-dimensional Banach space under nonlinear transformations of the space. We prove a general result concerning the
Continuous martingales and Brownian motion
• Mathematics
• 1990
0. Preliminaries.- I. Introduction.- II. Martingales.- III. Markov Processes.- IV. Stochastic Integration.- V. Representation of Martingales.- VI. Local Times.- VII. Generators and Time Reversal.-
On multidimensional stable processes with locally unbounded drift
• Mathematics
• 1995
A multidimensional stable process with a drift, which may be a locally unbounded function, is constructed.
On the martingale problem for generators of stable processes with perturbations
On ameliore les resultats de M. Tsuchiya en utilisant la theorie des integrales singulieres de Calderon et Zygmund