相关论文: The unique solution of stochastic differential equ…

Based on a compactness criterion for random fields in Wiener-Sobolev spaces, in this paper, we prove the unique strong solvability of time-inhomogeneous stochastic differential equations with drift coefficients in critical Lebesgue spaces,…

Direct and inverse problems for the Hirota difference equation are considered. Jost solutions and scattering data are introduced and their properties are presented. Darboux transformation in a special case is shown to give evolution with…

In the framework of fractional stochastic calculus, we study the existence and the uniqueness of the solution for a backward stochastic differential equation, formally written as: [{[c]{l}% -dY(t)= f(t,\eta(t),Y(t),Z(t))dt-Z(t)\delta…

We study the rate of convergence of an explicit and an implicit-explicit finite difference scheme for linear stochastic integro-differential equations of parabolic type arising in non-linear filtering of jump-diffusion processes. We show…

Stochastic thermodynamics is formulated for variables that are odd under time reversal. The invariance under spatial rotation of the collision rates due to the isotropy of the heat bath is shown to be a crucial ingredient. An alternative…

The geometrical theory of partial differential equations in the absolute sense, without any additional structures, is developed. In particular the symmetries need not preserve the hierarchy of independent and dependent variables. The order…

We prove existence and uniqueness of strong solutions to a large class of autonomous stochastic differential equations on an open domain, where the drift exhibits a singular behaviour at the boundary. The main result involves a drift…

The Schrodinger equation is considered with the first order time derivative changed to a Caputo fractional derivative, the time fractional Schrodinger equation. The resulting Hamiltonian is found to be non-Hermitian and non-local in time.…

We study linear backward stochastic partial differential equations of parabolic type with special boundary conditions in time. The standard Cauchy condition at the terminal time is replaced by a condition that holds almost surely and mixes…

In this paper, we study the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion (GSDEs) with integral-Lipschitz conditions on their coefficients.

We study an ordinary differential equation controlled by a stochastic process. We present results on existence and uniqueness of solutions, on associated local times (Trotter and Ray-Knight theorems), and on time and direction of…

Linear-quadratic optimal control problems are considered for mean-field stochastic differential equations with deterministic coefficients. Time-inconsistency feature of the problems is carefully investigated. Both open-loop and closed-loop…

We study the behaviour of solutions of ordinary differential equations of the second order with singular points, where the coefficients of the second-order derivative vanishes. In particular, we consider solutions entering a singular point…

Using direct variational method we consider the existence of non-spurious solutions to the following Dirichlet problem $\ddot{x}\left( t\right) =f\left( t,x\left( t\right) \right) $, $x\left( 0\right) =x\left( 1\right) =0 $ where $f:\left[…

We consider It\^o uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in $W^{1}_{d,loc}$, and the drift in $L_{d}$. We prove the unique strong solvability for any starting point and prove that as…

An algorithmic method to exploit a general class of infinitesimal symmetries for reducing stochastic differential equations is presented and a natural definition of reconstruction, inspired by the classical reconstruction by quadratures, is…

We provide explicit classical solutions and stochastic analogues for distributed-order space-time fractional diffusion equations on bounded domains with zero exterior boundary conditions. We also show that our results still hold when the…

We present a theory of backward stochastic differential equations in continuous time with an arbitrary filtered probability space. No assumptions are made regarding the left continuity of the filtration, of the predictable quadratic…

Based on the analysis of a certain class of linear operators on a Banach space, we provide a closed form expression for the solutions of certain linear partial differential equations with non-autonomous input, time delays and stochastic…

The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and…