• Corpus ID: 250089246

# L\'evy Flows and associated Stochastic PDEs

@inproceedings{Nath2022LevyFA,
title={L\'evy Flows and associated Stochastic PDEs},
author={Arvind Nath and Suprio Bhar},
year={2022}
}
• Published 28 June 2022
• Mathematics
In this paper, we first explore certain structural properties of Lévy flows and use this information to obtain the existence of strong solutions to a class of Stochastic PDEs in the space of tempered distributions, driven by Lévy noise. The uniqueness of the solutions follows from Monotonicity inequality. These results extend an earlier work [2] on the diffusion case.

## References

SHOWING 1-10 OF 11 REFERENCES

### Characterizing Gaussian Flows Arising from Itô’s Stochastic Differential Equations

In order to identify which of the strong solutions of Itô’s stochastic differential equations (SDEs) are Gaussian, we introduce a class of diffusions which ‘depend deterministically on the initial

### THE MONOTONICITY INEQUALITY FOR LINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

• Mathematics
• 2009
We prove the monotonicity inequality for differential operators A and L that occur as coefficients in linear stochastic partial differential equations associated with finite-dimensional Ito

### Differential operators on Hermite Sobolev spaces

• Mathematics
• 2015
In this paper, we compute the Hilbert space adjoint ∂∗ of the derivative operator ∂ on the Hermite Sobolev spaces Sq$\mathcal {S}_{q}$. We use this calculation to give a different proof of the

### Probabilistic Representations of Solutions of the Forward Equations

• Mathematics
• 2007
AbstractIn this paper we prove a stochastic representation for solutions of the evolution equation $$\partial _t \psi _t = \frac{1}{2}L^ * \psi _t$$ where L ∗  is the formal adjoint of a second

### Probabilistic representations of solutions to the heat equation

• Mathematics
• 2003
In this paper we provide a new (probabilistic) proof of a classical result in partial differential equations, viz. if ϕ is a tempered distribution, then the solution of the heat equation for the

### Lévy Processes and Stochastic Calculus

Levy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random

### Foundations of stochastic differential equations in infinite dimensional spaces

Multi-Hilbertian spaces and their dual spaces Infinite dimensional random variables and stochastic processes Infinite dimensional stochastic differential equations.

### Matrix analysis

• Mathematics
Statistical Inference for Engineers and Data Scientists
• 2018
This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications.

### Stochastic PDEs in S for SDEs driven by Lévy noise

• Random Oper. Stoch. Equ.,
• 2020

• 2002