In the present paper, we consider large scale nonsymmetric differential matrix Riccati equations with low rank right hand sides. These matrix equations appear in many applications such as control theory, transport theory, applied probability and others. We show how to apply Krylov-type methods such as the extended block Arnoldi algorithm to get low rank approximate solutions. The initial proble...

The classical Feynman-Kac formula states the connection between linear parabolic partial differential equations (PDEs), like the heat equation, and expectation of stochastic processes driven by Brownian motion. It gives then a method for solving linear PDEs by Monte Carlo simulations of random processes. The extension to (fully)nonlinear PDEs led in the recent years to important developments in...

A new Monte-Carlo method for solving linear parabolic partial differential equations is presented. Since, in this new scheme, the particles are followed backward in time, it provides great flexibility in choosing critical points in phase-space at which to concentrate the launching of particles and thereby minimizing the statistical noise of the sought solution. The trajectory of a particle, Xi(...

In this paper, we study a kind of Stackelberg game where the controlled systems are described by backward stochastic differential delayed equations (BSDDEs). By introducing new adjoint equation, establish sufficient verification theorem for optimal strategies leader and follower in general case. Then, focus on linear–quadratic (LQ) with delay. The equilibrium is presented generalized fully coup...

In this paper, we propose a class of nonlinear expectations induced by backward stochastic differential equations and reflected backward stochastic differential equations and prove the law of large numbers under the nonlinear expectation.

The DC analysis and transient analysis parts of the general electrical circuit analysis program ESACAP are parallelized to run on the Intel iPSC. Most of the program runs unchanged on the cube manager. Only the solution of the systems of nonlinear algebraic equations is parallelized to run on the hypercube parallel computer. The nonlinear equations arise either from the DC problem or from the d...

In this work, we establish the maximal [Formula: see text]-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order [Formula: see text], [Formula: see text], in time. These schemes include convolution quadratures generated by backward Euler method and second-order backward difference formula, the L1 scheme, explicit Euler met...

A new formula called 2-point diagonally implicit super class of BBDF with two off-step points (2ODISBBDF) for solving stiff IVPs is formulated. The method approximates two solutions with two off-step points simultaneously at each iteration. By varying a parameter ρ ∈ (–1,1) in the formula, different sets of formulae can be generated. A specific choice of 3 4 ρ = is made and it was shown that th...

<p style='text-indent:20px;'>This paper establishes an existence and uniqueness result for the adapted solution of a general time interval multidimensional backward stochastic differential equation (BSDE), where generator <inline-formula> <tex-math id="M1">\begin{document}$ g $\end{document}</tex-math> </inline-formula> satisfies weak stochastic-monotonicity condit...