• 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}
}
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

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

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

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

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

TLDR
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

Foundations of modern probability. Probability and its Applications (New York)

  • 2002