Related papers: Bismut Formula for Lions Derivative of Distributio…
To characterize the regularity of distribution-path dependent SDEs in the initial distribution which varies in the class of probability measures on the path space, we introduce the intrinsic and Lions derivatives for probability measures on…
By using distribution dependent Zvonkin's transforms and Malliavin calculus, the Bismut type formula is derived for the intrinisc/Lions derivatives of distribution dependent SDEs with singular drifts, which generalizes the corresponding…
In this paper we study a class of distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter H\in(1/2,1). We prove the well-posedness of this type equations, and then establish a…
By using the Malliavin calculus and solving a control problem, Bismut type derivative formulae are established for a class of degenerate diffusion semigroups with non-linear drifts. As applications, explicit gradient estimates and Harnack…
A Bismut type formula is established for the extrinsic derivative of distribution dependent SDEs. The main result is illustrated by nondegenerate DDSDEs with space time singular drift, as well as degenerate DDSDEs with weakly monotone…
In recent years, remarkable progress has been made for Distribution dependent stochastic equations (DDSDEs) with singular interactions, existing results include wellposedness, propagation of chaos, entropy cost inequality and ergodicity. As…
By using Malliavin calculus, explicit derivative formulae are established for a class of semi-linear functional stochastic partial differential equations with additive or multiplicative noise. As applications, gradient estimates and Harnack…
By using Malliavin calculus, Bismut derivative formulae are established for a class of stochastic (functional) differential equations driven by fractional Brownian motions. As applications, Harnack type inequalities and strong Feller…
The Bismut formula is a crucial tool characterizing regularities of stochastic systems, and has been extensively studied for various models. However it is not yet available for SDEs with distribution dependent noise. In this paper, we first…
In this paper, we investigate the regularities for a class of distribution dependent SDEs driven by two independent fractional noises $B^H$ and $\ti B^{\ti H}$ with Hurst parameters $H\in(0,1)$ and $\ti H\in(1/2,1)$. We establish the…
We analyze multi-dimensional mean-field stochastic differential equations where the drift depends on the law in form of a Lebesgue integral with respect to the pushforward measure of the solution. We show existence and uniqueness of…
In this work, we will show the existence, uniqueness, and weak differentiability of the solution to semi-linear mean-field stochastic differential equations driven by fractional Brownian motion. We prove an extension of the…
Let $(W,H,\mu)$ be the classical Wiener space on $\R^d$. Assume that $X=(X_t(x))$ is a diffusion process satisfying the stochastic differential equation with diffusion and drift coefficients $\sigma: \R^n\to \R^n\otimes \R^d$, $b: \R^n\to…
By solving a control problem and using Malliavin calculus, explicit derivative formula is derived for the semigroup $P_t$ generated by the Gruschin type operator on $\R^{m}\times \R^{d}:$ $$L (x,y)=\ff 1 2 \bigg\{\sum_{i=1}^m \pp_{x_i}^2…
We generalise the so-called Bismut-Elworthy-Li formula to a class of stochastic differential equations whose coefficients might depend on the law of the solution. We give some examples of where this formula can be applied to in the context…
In this paper we present a new interpretation of the Lions derivative as the Radon-Nikodym derivative of a vector measure, which provides a canonical extension of the Lions derivative for functions taking values in infinite dimensional…
We close an unexpected gap in the literature of stochastic differential equations (SDEs) with drifts of super linear growth (and random coefficients), namely, we prove Malliavin and Parametric Differentiability of such SDEs. The former is…
We consider a one-dimensional Stochastic Differential Equation with reflection where we allow the drift to be merely bounded and measurable. It is already known that such equations have a unique strong solution. Recently, it has been shown…
By establishing a local version of Bismut formula for Dirichlet semigroups on a regular domain, gradient estimates are derived for killed SDEs with singular drifts. As an application, the total variation distance between two solutions of…
Under nondegeneracy assumptions on the diffusion coefficients, we establish the derivative formulae of Bismut-Elworthy-Li's type for forward-backward stochastic differential equations with respect to Poisson random measure using the lent…