In this paper we consider a n-dimensional stochastic differential equation driven by a fractional Brownian motion with Hurst parameter H > 1/3. After solving this equation in a rather elementary way, following the approach of [10], we show how to obtain an expansion for E[f (X t)] in terms of t, where X denotes the solution to the SDE and f : R n → R is a regular function. With respect to [2], ...

The dynamics of proteins can be described as the superposition of motions at a continuum of time scales. In the special case of a protein immersed in an implicit solvent, a stochastic differential equation (SDE) can model the dynamics of the solute protein. Traditional model reduction techniques fail because a priori characterization of the slow variables in these SDEs is nearly impossible. We ...

In this paper, a stochastic flamelet approach is used to model autoignition in an initially non-premixed medium in isotropic and decaying turbulence, using a one-step irreversible reaction. This configuration corresponds to the DNS data from Sreedhara and Lakshmisha [Proc. Combust. Inst. 29 (2002) 2069]. The system can be described by the flamelet equations for the temperature and fuel mass fra...

We consider a dynamical system whose state equation evolves continuously in time according to a linear stochastic differential equation; the parameters of such SDE depend on a discrete variable that follows the laws of a continuous-time Markov process. Noisy measurements of the continuous state are made available at discrete deterministic times, by a static linear equation whose parameters depe...

Generating sample paths of stochastic differential equations (SDE) using the Monte Carlo method finds wide applications in financial engineering. Discretization is a popular approximate approach to generating those paths: it is easy to implement but prone to simulation bias. This article presents a new simulation scheme to exactly generate samples for SDEs. The key observation is that the law o...

a r t i c l e i n f o a b s t r a c t In this paper the stochastic differential equation (SDE) is utilized as a quantitative description of a natural phenomenon to distinguish normal and anomalous samples. In this framework, discrete samples are modeled as a continuous time-dependent diffusion process with time varying drift and diffusion coefficients. We employ a local non-parametric technique...

In this paper we consider a n-dimensional stochastic differential equation driven by a fractional Brownian motion with Hurst parameter H > 1/3. After solving this equation in a rather elementary way, following the approach of [10], we show how to obtain an expansion for E[f(Xt)] in terms of t, where X denotes the solution to the SDE and f : Rn → R is a regular function. With respect to [2], whe...

The origin of the long-range memory in non-equilibrium systems is still an open problem as the phenomenon can be reproduced using models based on Markov processes. In these cases, the notion of spurious memory is introduced. A good example of Markov processes with spurious memory is a stochastic process driven by a non-linear stochastic differential equation (SDE). This example is at odds with ...

The evolution of a quantum system subject to continuous weak measurement is described by stochastic differential equation (SDE). It has been shown that the conventional density matrix ρ t $\rho _t$ characterized such SDE, under experimentally relevant settings, remains within deterministically evolving manifold low dimension, whose associated equations can be computed explicitly. In this paper,...

A warrant is a derivative that gives the right, but not obligation, to buy or sell security at certain price before expiration. The valuation method was inspired by option because of similarities between these two derivatives. formula under Black–Scholes available in literature. However, known have number flaws; hence, this study aims develop pricing for warrants incorporating jumps, stochastic...