The χ language is a hybrid language for modeling, simulation and verification. As a result of the recently completed formal semantics, the language now consists of a number of orthogonal operators that operate on all process terms, including differential algebraic equations. The same χ model can be used for simulation and verification. Verification is possible after a straightforward syntactica...

If a model structure is not identifiable, then it is not possible to uniquely identify its parameters from measured data. This contribution describes how solvers for differential-algebraic equations (DAE) can be used to examine if a model structure is locally identifiable. The procedure can be applied to both linear and nonlinear systems. If a model structure is not identifiable, it is also pos...

Considering the hydrodynamical limit of some interacting particle systems leads to hyperbolic differential equation for the conserved quantities, e.g. the inviscid Burgers equation for the simple exclusion process. The physical solutions of these partial differential equations develop discontinuities, called shocks. The microscopic structure of these shocks is of much interest and far from bein...

In this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. The homotopy analysis method (HAM) is used for solving this equation. Several examples are given to reconfirm the efficiency of these algorithms. The results of applying this procedure...

We consider stochastic differential equations on the whole Euclidean space possessing a scalar invariant along their solutions. The stochastic dynamics therefore evolves on a hypersurface of the ambient space. Using orthogonal coordinate systems, we show the existence and uniqueness of smooth solutions of the Kolmogorov equation under some ellipticity conditions over the invariant hypersurfaces...

We discuss the use of the formal theory of differential equations in the numerical analysis of general systems of partial differential equations. This theory provides us with a very powerful and natural framework for generalising many ideas from differential algebraic equations to partial differential equations. We study in particular the existence and uniqueness of (formal) solutions, the meth...

Suppose that d ≥ 2 and α ∈ (1, 2). Let μ = (μ, . . . , μ) be such that each μ is a signed measure on R belonging to the Kato class Kd,α−1. In this paper, we consider the stochastic differential equation dXt = dSt + dAt, where St is a symmetric α-stable process on R and for each j = 1, . . . , d, the j-th component of At is a continuous additive functional of finite variation with respect to X w...

We define the Burgers superprocess to be the solution of the stochastic partial differential equation ∂ ∂t u(t, x) =∆u(t, x) − λu(t, x)∇u(t, x) + γ √ u(t, x) W (dt, dx), where t ≥ 0, x ∈ R, and W is space-time white noise. Taking γ = 0 gives the classic Burgers equation, an important, non-linear, partial differential equation. Taking λ = 0 gives the super Brownian motion, an important, measure ...

We consider a (B, S)-security market with standard riskless asset B(t) = B0ert and risky asset S(t) with stochastic volatility depending on time t and the history of stock price over the interval [t − τ, t]. The stock price process S(t) satisfies a stochastic delay differential equation (SDDE) with past-dependent diffusion coefficient. We state some results on option pricing in such a market an...