This thesis has as main aims: • analyzing the effects of nonlinearities and stochasticity on price dynamics of assets, in general, • modeling the price dynamics of oil, as a special commodity, • determining option prices and optimal hedging strategies for commodities like oil. In many economic and financial processes mathematical modeling leads to nonlinear and stochastic dynamical systems. The...

In transducing mechanical stimuli into electrical signals, at least some hair cells in vertebrate auditory and vestibular systems respond optimally to weak periodic signals at natural, nonzero noise intensities. We understand this stochastic resonance by constructing a faithful mechanical model reflecting the hair cell geometry and described by a nonlinear stochastic differential equation. This...

The general method of Lyapunov functionals construction has been developed during the last decade for stability investigations of stochastic differential equations with aftereffect and stochastic difference equations. After some modification of the basic Lyapunov type theorem this method was successfully used also for difference Volterra equations with continuous time. The latter often appear a...

We study the relation between stochastic and continuous transport-limited growth models. We derive a nonlinear integro-differential equation for the average shape of stochastic aggregates, whose mean-field approximation is the corresponding continuous equation. Focusing on the advection-diffusion-limited aggregation (ADLA) model, we show that the average shape of the stochastic growth is simila...

chloride ion ingress in concrete is the main reason of concrete corrosion. in real world both uncertainty and stochasticity are main attributes of almost all measurements including testing and modeling of chloride content profile in concrete. regarding these facts new models should be able to represent at least some of the uncertainties in the predictions. in this paper after inspiration from c...

The limit cycles of nonlinear systems under the small stochastic disturbances are considered. The random trajectories of forced system leave the deterministic cycle and form some stochastic bundle around it. The probabilistic description of this bundle near cycle based on stochastic sensitivity function (SSF) is suggested. The SSF is a covariance matrix for periodic solution of linear stochasti...

in this paper, we implemented the modified iteration perturbation method (mipm) for approximating the periodic behavior of a tapered beam. this problem is formulated as a nonlinear ordinary differential equation with linear and nonlinear terms. the solution is quickly convergent and does not need to complicated calculations. comparing the results of the mipm with the exact solution shows that t...

Motivated by the recent advances in the theory of stochastic partial differential equations involving nonlinear functions of distributions, like the Kardar-Parisi-Zhang (KPZ) equation, we reconsider the unique solvability of one-dimensional stochastic differential equations, the drift of which is a distribution, by means of rough paths theory. Existence and uniqueness are established in the wea...

This paper derives Hamilton-Jacobi equation (HJE) in Hilbert space for optimal control of stochastic distributed parameter systems (SDPSs) governed by partial differential equations (SPDEs) subject to both state-dependent and additive stochastic disturbances. First, nonlinear SDPSs are transformed to stochastic evolution systems (SESs), which are governed by stochastic ordinary differential equ...