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Register a new userDistribution Dependent SDEs with H{o}lder Continuous Drift and $alpha$-Stable Noise
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In this paper, the existence and uniqueness of the distribution dependent SDEs with H{o}lder continuous drift driven by $alpha$-stable process is investigated. Moreover, by using Zvonkin type transformation, the convergence rate of Euler-Maruyama method is also obtained. The results cover the ones in the case of distribution independent SDEs.
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We study distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [16]. We provide several criteria for existence and uniqueness of solutions which go beyond the classical globally Lipschitz setting. In particular we show well-posedness of the equation, as well as almost sure convergence of the associated particle system, for drifts satisfying either Osgood-continuity, monotonicity, local Lipschitz or Sobolev differentiability type assumptions.
By using the technique of the Zvonkins transformation and the classical Khasminkiis time discretization method, we prove the averaging principle for slow-fast stochastic partial differential equations with bounded and H{o}lder continuous drift coefficients. An example is also provided to explain our result.
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 Holder 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 Holder 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.
In this paper we prove the existence of strong solutions to a SDE with a generalized drift driven by a multidimensional fractional Brownian motion for small Hurst parameters H<1/2. Here the generalized drift is given as the local time of the unknown solution process, which can be considered an extension of the concept of a skew Brownian motion to the case of fractional Brownian motion. Our approach for the construction of strong solutions is new and relies on techniques from Malliavin calculus combined with a local time variational calculus argument.
In this paper, the discrete parameter expansion is adopted to investigate the estimation of heat kernel for Euler-Maruyama scheme of SDEs driven by {alpha}-stable noise, which implies krylovs estimate and khasminskiis estimate. As an application, the convergence rate of Euler-Maruyama scheme of a class of multidimensional SDEs with singular drift( in aid of Zvonkins transformation) is obtained.
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