Abstract. We present various versions of the maximum principle for optimal control of forwardbackward stochastic differential equations (SDE) with jumps. Our study is motivated by risk minimization via g-expectations. We first prove a general sufficient maximum principle for optimal control with partial information of a stochastic system consisting of a forward and a backward SDE driven by Lévy...

We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simultaneously under a family of singular measures, rather than the usual family of processes indexed by the controls. This value process is characterized by a second order backward SDE, which can be seen...

Suppose that a real valued process X is given as a solution to a stochastic differential equation. Then, for any twice continuously differentiable function f , the backward Kolmogorov equation gives a condition for f(t,X) to be a local martingale. We generalize the backward equation in two main ways. First, it is extended to non-differentiable functions. Second, the process X is not required to...

Stochastic diffusion is a general phenomenon observed in various national and engineering systems. It is typically modeled by either stochastic differential equation (SDE) or Fokker-Planck equation (FPE), which are equivalent approaches. Path integral is an accurate and effective method to solve FPEs. Yet, computational efficiency is the common challenge for path integral and other numerical me...

in this paper, we intend to solve special kind of ordinary differential equations which is called heun equations, by converting to a corresponding stochastic differential equation(s.d.e.). so, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this s.d.e. is solved by numerically methods. mo...

We establish a connection between two population models by showing that one is the scaling limit of other, as grows large. In infinite model, individuals are split into subpopulations, carrying either selective advantageous allele, or disadvantageous one. The proportion disadvantaged in evolves according to Λ-Wright–Fisher stochastic differential equation (SDE) with selection, and genealogy des...

Differential equations have long been used to describe the motion of particles. Stochastic differential equations (SDE)s have been employed for situations where randomness is included. This present work is motivated in part by seeking to describe the motion of mammals moving in a constrained region. Interesting questions that arise include: how to write down a pertinent (bivariate) SDE, how to ...

We study inference for the driving Lévy noise of an ergodic stochastic differential equation (SDE) model, when process is observed at high-frequency and long time drift scale coefficients contain finite-dimensional unknown parameters. By making use Gaussian quasi-likelihood function coefficients, we derive a expansion functionals unit-time residuals, which clarifies some quantitative effect plu...

We develop an Explicitly Solvable Energy-Conserving (ESEC) algorithm for the Stochastic Differential Equation (SDE) describing pitch-angle scattering process in magnetized plasmas. The Cayley transform is used to calculate both deterministic gyromotion and stochastic scattering, affording be explicitly solvable exactly energy conserving. An unusual property of SDE that its coefficients diverge ...

Parametric rolling is one of the dangerous dynamic phenomena. To discuss safety a vessel when phenomenon occurs, it important to estimate probability certain dynamical behavior ship with respect threshold level. In this paper, moment values are obtained by solving equations. Since stochastic differential equation (SDE) needed obtain equations, autoregressive moving average (ARMA) filter used. T...