23,656 research outputs found
A new approach to BSDE
Key words: Backward stochastic differential equation, semimartingale, comparison\ud
theorem, ordinary functional differential equation, stochastic differential equation, local\ud
condition, homogeneous property, K-Lipschitz conditio
Adiabatic elimination in quantum stochastic models
We consider a physical system with a coupling to bosonic reservoirs via a
quantum stochastic differential equation. We study the limit of this model as
the coupling strength tends to infinity. We show that in this limit the
solution to the quantum stochastic differential equation converges strongly to
the solution of a limit quantum stochastic differential equation. In the
limiting dynamics the excited states are removed and the ground states couple
directly to the reservoirs.Comment: 17 pages, no figures, corrected mistake
A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise
We study a least square-type estimator for an unknown parameter in the drift
coefficient of a stochastic differential equation with additive fractional
noise of Hurst parameter H>1/2. The estimator is based on discrete time
observations of the stochastic differential equation, and using tools from
ergodic theory and stochastic analysis we derive its strong consistency.Comment: 15 page
Identification and estimation of continuous time dynamic systems with exogenous variables using panel data
This paper deals with the identification and maximum likelihood estimation of the parameters of a stochastic differential equation from discrete time sampling. Score function and maximum likelihood equations are derived explicitly. The stochastic differential equation system is extended to allow for random effects and the analysis of panel data. In addition, we investigate the identifiability of the continuous time parameters, in particular the impact of the inclusion of exogenous variables
Optimal bounds for the densities of solutions of SDEs with measurable and path dependent drift coefficients
We consider a process given as the solution of a stochastic differential
equation with irregular, path dependent and time-inhomogeneous drift
coefficient and additive noise. Explicit and optimal bounds for the Lebesgue
density of that process at any given time are derived. The bounds and their
optimality is shown by identifying the worst case stochastic differential
equation. Then we generalise our findings to a larger class of diffusion
coefficients.Comment: 24 pages and 1 figur
On the Aggregation of Inertial Particles in Random Flows
We describe a criterion for particles suspended in a randomly moving fluid to
aggregate. Aggregation occurs when the expectation value of a random variable
is negative. This random variable evolves under a stochastic differential
equation. We analyse this equation in detail in the limit where the correlation
time of the velocity field of the fluid is very short, such that the stochastic
differential equation is a Langevin equation.Comment: 16 pages, 2 figure
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