Related papers: Multivalued backward stochastic differential equat…

In this paper, we deal with a class of mean-field backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We obtain the existence and uniqueness theorem and a comparison theorem for…

In this paper we investigate in a Hilbert space setting a second order dynamical system of the form $$\ddot{x}(t)+\g(t)\dot{x}(t)+x(t)-J_{\lambda(t) A}\big(x(t)-\lambda(t) D(x(t))-\lambda(t)\beta(t)B(x(t))\big)=0,$$ where $A:{\mathcal…

We study an optimal control problem on infinite horizon for a controlled stochastic differential equation driven by Brownian motion, with a discounted reward functional. The equation may have memory or delay effects in the coefficients,…

In the paper, we consider the no-explosion condition and pathwise uniqueness for SDEs driven by a Poisson random measure with coefficients that are super-linear and non-Lipschitz. We give a comparison theorem in the one-dimensional case…

The rates of strong convergence for various approximation schemes are investigated for a class of stochastic differential equations (SDEs) which involve a random time change given by an inverse subordinator. SDEs to be considered are unique…

In this paper, we study the well-posedness and regularity of non-autonomous stochastic differential algebraic equations (SDAEs) with nonlinear, locally Lipschitz and monotone (2) coefficients of the form (1). The main difficulty is the fact…

This work focuses on multivalued stochastic differential equations with jumps. First, by employing the weak convergence approach, we establish the Freidlin-Wentzell uniform large deviation principle and the Dembo-Zeitouni uniform large…

In this paper we consider the maximum principle of optimal control for a stochastic control problem. This problem is governed by a system of fully coupled multi-dimensional forward-backward doubly stochastic differential equation with…

This paper solves a recursive optimal stopping problem with Poisson stopping constraints using the penalized backward stochastic differential equation (PBSDE) with jumps. Stopping in this problem is only allowed at Poisson random…

In this paper we investigate a kind of optimal control problem of coupled forward-backward stochastic system with jumps whose cost functional is defined through a coupled forward-backward stochastic differential equation with Brownian…

For the time development of a single system in the quantum jump approach or for quantum trajectories one requires the conditional (reduced) Hamiltonian between jumps and the reset operator after a jump. Explicit expressions for them are…

We study the existence and uniqueness of a solution for the multivalued stochastic differential equation with delay (the multivalued term is of subdifferential type): \[ \left\{\begin{array} [c]{r} dX(t)+\partial\varphi\left(X(t)\right)…

In this paper, we investigate new sufficient conditions to ensure the existence of a unique global strong solution of stochastic differential equations with jumps. By using Euler approximation and by utilising a new test function…

This article addresses a new class of fractional nonlocal neutral stochastic differential system of order 1<q<2 including non-instantaneous impulses(NIIs) and state-dependent delay(SDD) with the Poisson jumps and the Wiener process in…

We propose and analyze the convergence of a novel stochastic algorithm for solving monotone inclusions that are the sum of a maximal monotone operator and a monotone, Lipschitzian operator. The propose algorithm requires only unbiased…

In this paper, a class of generalized backward doubly stochastic differential equations whose coefficient contains the subdifferential operators of two convex functions (also called generalized backward doubly stochastic variational…

In this paper, we consider the stochastic averaging principle and stability for multi-valued McKean-Vlasov stochastic differential equations with jumps. First, under certain averaging conditions, we are able to show that the solutions of…

We introduce an explicit adaptive Milstein method for stochastic differential equations (SDEs) with no commutativity condition. The drift and diffusion are separately locally Lipschitz and together satisfy a monotone condition. This method…

In a noise driving by a multivariate point process $\mu$ with predictable compensator $\nu$, we prove existence and uniqueness of the reflected backward stochastic differential equation's solution with a lower obstacle…

In this paper, we study the convergence for solutions to a sequence of (possibly degenerate) stochastic differential equations with jumps, when the coefficients converge in some appropriate sense. Our main tools are the superposition…