On strong solutions and explicit formulas for solutions of stochastic integral equations

TL;DR: In this paper, the effects of the propagation of a non-degenerate Brownian noise through a chain of deterministic differential equations whose coefficients are rough and satisfy a weak like Hormander structure were investigated.

TL;DR: In this paper , the authors investigated the well-posedness of the martingale problem associated to non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov under mild assumptions on the coefficients as well as classical solutions for a class of associated linear PDEs defined on [0,T]×Rd×P2(Rd), for any T>0, P2(rd) being the Wasserstein space.

TL;DR: In this paper, the existence and uniqueness of mild solutions for a class of degenerate stochastic differential equations on Hilbert spaces where the drift is Dini continuous in the component with noise and Holder continuous of order larger than 2 3 in the other component were proved.

TL;DR: Da Prato et al. as discussed by the authors generalized Veretennikov's fundamental result to infinite dimensions assuming boundedness of the drift term and proved pathwise uniqueness in the class of global solutions.

TL;DR: In this paper, a quasi-isometric transformation of a phase space that allows passing from a diffusion process with nonzero drift coefficient to a process without drift is presented, and strong solutions of stochastic differential equations with a "bad" drift coefficient are constructed.

TL;DR: In this paper, the authors prove the existence of a strong solution of a stochastic integral equation of the form, using the theory of differential equations of parabolic type, and prove the proof of these criteria is based on finding formulas expressing via multiple Stochastic integrals, formulas which in the case give an expression for, if is a strong solutions of the stochastically equation.