This paper provides a large deviation principle for Non-Markovian, Brownian motion driven stochastic di↵erential equations with random coe cients. Similar to Gao & Liu [19], this extends the corresponding results collected in Freidlin & Wentzell [18]. However, we use a di↵erent line of argument, adapting the PDE method of Fleming [14] and Evans & Ishii [10] to the pathdependent case, by using b...

Stochastic di erential games are considered in a non-Markovian setting. Typically, in stochastic di erential games the modulating process of the di usion equation describing the state ow is taken to be Markovian. Then Nash equilibria or other types of solution such as Pareto equilibria are constructed using Hamilton-Jacobi-Bellman (HJB) equations. But in a non-Markovian setting the HJB method i...

The following backward stochastic Riccati di erential equation (BSRDE in short) 8>>>>><>>>>>>>>>>>: dK = [AK +KA+ d X i=1 C 0 iKCi +Q+ d X i=1 (C 0 iLi + LiCi)

— We present necessary and su‰cient conditions to guarantee that at least one solution of an infinite dimensional stochastic di¤erential equation, which starts from a regular closed subset K of an Hilbert space, remains in K for all times.

in this paper, we study rst order linear fuzzy dierential equations with fuzzy coecient and initial value. we use the generalized dierentiability concept and apply the exponent matrix to present the general form of their solutions. finally, one example is given to illustrate our results.

We simulate the Kardar-Parisi-Zhang equation in 2+1 dimensions. It is a non linear stochastic di erential equation which describes driven growing interfaces. The Hopf-Cole transformation is used in order to obtain a stable numerical scheme. The two relevant critical exponents are precisely measured. PACS numbers: 64.60.Ht, 05.40.+j, 05.70.Ln, 68.35.Fx

Degenerate parabolic equations of Kolmogorov type occur in many areas of analysis and applied mathematics. In their simplest form these equations were introduced by Kolmogorov in 1934 to describe the probability density of the positions and velocities of particles but the equations are also used as prototypes for evolution equations arising in the kinetic theory of gases. More recently equation...

This work presents the arguments for the possibility of approximating some discontinuous dynamical systems with continuous or even smooth dynamical systems. The discontinuous di€erential equation, which describes the system, is transformed into a di€erential inclusion and then into a di€erential equation with continuous or smooth right-hand side. As an example a generalization of the equations ...

Di€usion and convection coecients of the aerated ̄ow in a hydraulic jump are estimated in the framework of an optimal control problem. The speci®c gravity of air±water mixture is governed by a steady state convection di€usion partial di€erential equation. The governing equation includes the di€usion coecient and the convection coecient, which are taken as the control variables to minimize a ...

Keywords: estimation, maximum principle, stochastic di¤erential equation, time-varying parameters. An important area of …nancial mathematics studies the expected returns and volatilities of the price dynamics of stocks, bonds, and interest rates. The stochastic dynamics of stocks, bonds, and interest rates should be correctly speci…ed since misspeci…cation of a model leads to erroneous valuatio...