Related papers: Stochastic functional differential equations drive…
Sufficient and necessary conditions are presented for the order-preservation of stochastic functional differential equations on $\R^d$ with non-Lipschitzian coefficients driven by the Brownian motion and Poisson processes. The sufficiency…
We deduce stability and pathwise uniqueness for a McKean-Vlasov equation with random coefficients and a multidimensional Brownian motion as driver. Our analysis focuses on a non-Lipschitz drift coefficient and includes moment estimates for…
We consider stochastic differential equations (SDEs) driven by a fractional Brownian motion with a drift coefficient that is allowed to be arbitrarily close to criticality in a scaling sense. We develop a comprehensive solution theory that…
In this paper, we consider a reflected backward stochastic differential equation driven by a $G$-Brownian motion ($G$-BSDE), with the generator growing quadratically in the second unknown. We obtain the existence by the penalty method, and…
We consider a system of stochastic differential equations driven by a standard n-dimensional Brownian motion where the drift coefficient satisfies a Novikov-type condition while the diffusion coefficient is the identity matrix. We define a…
In this paper, we study a class of one-dimensional stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H>\ff 1 2$. The drift term of the equation is locally Lipschitz and unbounded in the…
This paper is concerned with the initial-boundary value problem \; for stochastic transport equations in bounded domains. For a given stochastic perturbation of the drift vector field, we prove existence and uniqueness of weak solutions…
We show that any stochastic differential equation (SDE) driven by Brownian motion with drift satisfying the Krylov-R\"ockner condition has exactly one solution in an ordinary sense for almost every trajectory of the Brownian motion.…
Existence, uniqueness, and $L_p$-approximation results are presented for scalar stochastic differential equations (SDEs) by considering the case where, the drift coefficient has finitely many spatial discontinuities while both coefficients…
This paper is concerned with a class of uncertain backward stochastic differential equations (UBSDEs) driven by both an $m$-dimensional Brownian motion and a $d$-dimensional canonical process with uniform Lipschitzian coefficients. Such…
We investigate stochastic processes that generalize geometric Brownian motion, focusing on cases where the standard invariant measure, i.e. the solution of the stationary Fokker-Planck equation does not necessarily exist. We demonstrate…
This paper is devoted to studying the properties of the exit times of stochastic differential equations driven by $G$-Brownian motion ($G$-SDEs). In particular, we prove that the exit times of $G$-SDEs has the quasi-continuity property. As…
The existence of stationary distributions to distribution dependent stochastic differential equations are investigated by using the ergodicity of the associated decoupled equation and the Schauder fixed point theorem. By using Zvonkin's…
We prove existence and uniqueness of strong solutions, as well as continuous dependence on the initial datum, for a class of fully nonlinear second-order stochastic PDEs with drift in divergence form. Due to rather general assumptions on…
We present an existence theory for martingale and strong solutions to doubly nonlinear evolution equations in a separable Hilbert space in the form $$d(Au) + Bu\,dt \ni F(u)\,dt + G(u)\,dW$$ where both $A$ and $B$ are maximal monotone…
Sticky Brownian motion on the real line can be obtained as a weak solution of a system of stochastic differential equations. We find the conditional distribution of the process given the driving Brownian motion, both at an independent…
We survey recent developments in the field of complexity of pathwise approximation in $p$-th mean of the solution of a stochastic differential equation at the final time based on finitely many evaluations of the driving Brownian motion.…
In this paper, we study the multi-dimensional reflected backward stochastic differential equation driven by $G$-Brownian motion ($G$-BSDE) with a multi-variate constraint on the $G$-expectation of its solution. The generators are diagonally…
The main result of the present paper is a statement on existence, uniqueness and regularity for mild solutions to a parabolic transport diffusion type equation that involves a non-smooth coefficient. We investigate related Cauchy problems…
Consider in a real Hilbert space $H$ the differential equation (inclusion) $(E)$: $p(t)u^{\prime \prime}(t)+q(t)u^{\prime}(t)\in Au(t)+f(t)$ for a.a. $t>0$, with the condition $(B)$: $u(0)=x \in \overline{D(A)}$, where $A\colon D(A)\subset…