Related papers: Stochastic differential equations with path-indepe…

We prove the existence of a weak solution to a backward stochastic differential equation (BSDE) $$ Y_t=\xi+\int_t^T f(s,X_s,Y_s,Z_s)\,ds-\int_t^T Z_s\,d\wien_s$$ in a finite-dimensional space, where $f(t,x,y,z)$ is affine with respect to…

This paper considers a general one-dimensional stochastic differential equation (SDE). A particular attention is given to the SDEs that may be transformed (via Ito's formula) into:$$d X\_t = ( \bar{B} (X\_t) - b X\_t) d t + \sqrt{X\_t} d…

A representation formula for solutions of stochastic partial differential equations with Dirichlet boundary conditions is proved. The scope of our setting is wide enough to cover the general situation when the backward characteristics that…

In this paper, we prove that there exists a unique strong solution to reflecting stochastic differential equations with merely measurable drift giving an affirmative answer to the longstanding problem. This is done through Zvonkin…

We consider non-linear time-fractional stochastic heat type equation $$\partial^\beta_tu_t(x)=-\nu(-\Delta)^{\alpha/2} u_t(x)+I^{1-\beta}_t[\sigma(u)\stackrel{\cdot}{W}(t,x)]$$ in $(d+1)$ dimensions, where $\nu>0, \beta\in (0,1)$,…

In this paper we give a necessary and suffcient conditions for the existence and uniqueness of periodic solutions of functional differential equations with n delay d dt x(t) = Ax(t) + n j=1 Bx(t -- r j) + f (t). The conditions are obtained…

We consider the use of adaptive timestepping to allow a strong explicit Euler-Maruyama discretisation to reproduce dynamical properties of a class of nonlinear stochastic differential equations with a unique equilibrium solution and…

A Milstein-type method is proposed for some highly non-linear non-autonomous time-changed stochastic differential equations (SDEs). The spatial variables in the coefficients of the time-changed SDEs satisfy the super-linear growth condition…

In this paper we introduce a model, the stochastic fractional delay differential equation (SFDDE), which is based on the linear stochastic delay differential equation and produces stationary processes with hyperbolically decaying…

Let u = {u(t, x), t $\in$ [0, T ], x $\in$ R d } be the solution to the linear stochastic heat equation driven by a fractional noise in time with correlated spatial structure. We study various path properties of the process u with respect…

We consider the following stochastic space-time fractional diffusion equation with vanishing initial condition:$$ \partial^{\beta} u(t, x)=- \left(-\Delta\right)^{\alpha / 2} u(t, x)+ I_{0+}^{\gamma}\left[\dot{W}(t, x)\right],\quad…

In this paper we will study the existence and uniqueness of the solution for the stochastic variational inequality with oblique subgradients of the following form:{l} dX_{t}+H(X_{t}) \partial \phi (X_{t}) (dt) \ni f(t,X_{t}) dt+g(t,X_{t})…

The solvability of a delay differential equation arising in the construction of quadratic cost functionals, i.e. Lyapunov functionals, for a linear time-delay system with a constant and a distributed delay is investigated. We present a…

Consider the following stochastic partial differential equation, \begin{equation*} \partial_t u_t(x)= \mathcal{L}u_t(x)+ \xi\sigma (u_t(x)) \dot F(t,x), \end{equation*} where $\xi$ is a positive parameter and $\sigma$ is a globally…

We consider backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We show that appropriate solutions exist for arbitrary terminal conditions, and are unique up to sets of measure zero. We…

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.…

We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…

Let $(B_t)_{t\in[0,\infty)}$ be a Brownian motion on a probability space $(\Omega,\mathcal{F},P)$. Our concern is whether and how a noncausal type stochastic differential $dX_t=a(t,\omega)\,dB_t+b(t,\omega)\,dt$ is identified from its…

This paper is to investigate if the solution of a hybrid stochastic functional differential equation (SFDE) with infinite delay can be approximated by the solution of the corresponding hybrid SFDE with finite delay. A positive result is…

We prove that the standard conditions that provide unique solvability of a mixed stochastic differential equations also guarantee that its solution possesses finite moments. We also present conditions supplying existence of exponential…