A simple method for the existence of a density for stochastic evolutions with rough coefficients

Romito, Marco

doi:10.1214/18-ejp242

Cited by 24 publications

(48 citation statements)

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“…As mentioned in introduction, Romito [57] studied the existence and Besov regularity of the probability density function of a solution of SDEs with locally bounded drift, and locally Hölder continuous, elliptic diffusion coefficient. Therefore, the statement of Theorem 4.3 isincluded in their results (see, Theorem 4.1 in [57]). In [57], Romito use a localization argument and one-step Euler-Maruyama scheme.…”

Section: One-dimensional Sdes With Super-linear Growth Coefficientsmentioning

confidence: 99%

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Probability density function of SDEs with unbounded and path-dependent drift coefficient

Taguchi

Tanaka

2020

Stochastic Processes and their Applications

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In this paper, we first prove that the existence of a solution of SDEs under the assumptions that the drift coefficient is of linear growth and path-dependent, and diffusion coefficient is bounded, uniformly elliptic and Hölder continuous. We apply Gaussian upper bound for a probability density function of a solution of SDE without drift coefficient and local Novikov condition, in order to use Maruyama-Girsanov transformation. The aim of this paper is to prove the existence with explicit representations (under linear/super-linear growth condition), Gaussian two-sided bound and Hölder continuity (under sub-linear growth condition) of a probability density function of a solution of SDEs with path-dependent drift coefficient. As an application of explicit representation, we provide the rate of convergence for an Euler-Maruyama (type) approximation, and an unbiased simulation scheme. = σ(t, Y 0,x t )dW t , Y 0,x 0 = x and "local" Novikov condition, in order to use Maruyama-Girsanov transformation. We will also show that the existence of a pdf

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Section: One-dimensional Sdes With Super-linear Growth Coefficientsmentioning

confidence: 99%

“…Therefore, the statement of Theorem 4.3 isincluded in their results (see, Theorem 4.1 in [57]). In [57], Romito use a localization argument and one-step Euler-Maruyama scheme. On the other hand, in our paper, we use directly one-step tamed Euler scheme, so the approach of proof is different.…”

Section: One-dimensional Sdes With Super-linear Growth Coefficientsmentioning

confidence: 99%

Probability density function of SDEs with unbounded and path-dependent drift coefficient

Taguchi

Tanaka

2020

Stochastic Processes and their Applications

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“…Our main tool to get the existence and the regularity of the density of the solution to (3) is the following smoothing lemma from [8].…”

Section: Fractional Integration By Partsmentioning

confidence: 99%

“…We will deal separately with the summands Pe and Ae, by using the ideas from [8] and the properties of the Volterra noise B.…”

Section: The Existence and The Besov Regularity Of The Densitymentioning

confidence: 99%

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Existence and Besov regularity of the density for a class of SDEs with Volterra noise

Olivera

Tudor

2019

Comptes Rendus. Mathématique

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Well‐posedness of diffusion–aggregation equations with bounded kernels and their mean‐field approximations

Chen,

Nikolaev,

Prömel

2024

Math Methods in App Sciences

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The well‐posedness and regularity properties of diffusion–aggregation equations, emerging from interacting particle systems, are established on the whole space for bounded interaction force kernels by utilizing a compactness convergence argument to treat the nonlinearity as well as a Moser iteration. Moreover, we prove a quantitative estimate in probability with arbitrary algebraic rate between the approximative interacting particle systems and the approximative McKean–Vlasov SDEs, which implies propagation of chaos for the interacting particle systems.

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A simple method for the existence of a density for stochastic evolutions with rough coefficients

Abstract: We extend the validity of a simple method for the existence of a density for stochastic differential equations, first introduced in [14], by proving local estimate for the density, existence for the density with summable drift, and by improving the regularity of the density.

Cited by 24 publications

References 50 publications

Probability density function of SDEs with unbounded and path-dependent drift coefficient

Probability density function of SDEs with unbounded and path-dependent drift coefficient

Existence and Besov regularity of the density for a class of SDEs with Volterra noise

Well‐posedness of diffusion–aggregation equations with bounded kernels and their mean‐field approximations

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