Convergence of Passive Scalars in Ornstein-uhlenbeck Flows to Kraichnan’s Model

Convergence of Passive Scalar Fields in OrnsteinUhlenbeck Flows to Kraichnan's Model

We prove that the passive scalar field in the Ornstein-Uhlenbeck velocity field with wave-number dependent correlation times converges, in the white-noise limit, to that of Kraichnan’s model with higher spatial regularity.

Invariant Measures for Passive Tracer Dynamics in Ornstein-uhlenbeck Flows

Diffusion Approximation of Recurrent Schemes for Financial Markets, with Application to the Ornstein-uhlenbeck Process

We adapt the general conditions of the weak convergence for the sequence of processes with discrete time to the diffusion process towards the weak convergence for the discrete-time models of a financial market to the continuous-time diffusion model. These results generalize a classical scheme of the weak convergence for discrete-time markets to the Black-Scholes model. We give an explicit and d...

Turbulence for (and By) Amateurs

4. Series of lectures on statistical turbulence written for amateurs but not experts. Elementary aspects and problems of turbulence in two and three dimensional Navier-Stokes equation are introduced. A few properties of scalar turbulence and transport phenomena in turbulent flows are described. Kraichnan’s model of passive advection is discussed a bit more precisely. Part 1: Approaching turbule...

Undamped Harmonic Oscillator Driven by Additive Gaussian White Noise: a Statistical Analysis

While consistency of the maximum likelihood estimator of the drift matrix in a multi-dimensional continuous time Ornstein-Uhlenbeck process holds under rather general conditions, little is known about the rate of convergence and the limiting distribution of the estimator when the underlying process is not ergodic. The objective of the paper is to investigate these questions for an important exa...