28 research outputs found
Uniform exponential ergodicity of stochastic dissipative systems
We study ergodic properties of stochastic dissipative systems with additive
noise. We show that the system is uniformly exponentially ergodic provided the
growth of nonlinearity at infinity is faster than linear. The abstract result
is applied to the stochastic reaction diffusion equation in with
.Comment: 16 page
Ergodicity of Stochastically Forced Large Scale Geophysical Flows
We investigate the ergodicity of 2D large scale quasigeostrophic flows under
random wind forcing. We show that the quasigeostrophic flows are ergodic under
suitable conditions on the random forcing and on the fluid domain, and under no
restrictions on viscosity, Ekman constant or Coriolis parameter. When these
conditions are satisfied, then for any observable of the quasigeostrophic
flows, its time average approximates the statistical ensemble average, as long
as the time interval is sufficiently long
A pricing formula for delayed claims: Appreciating the past to value the future
We consider the valuation of contingent claims with delayed dynamics in a
Black \& Scholes complete market model. We find a pricing formula that can be
decomposed into terms reflecting the market values of the past and the present,
showing how the valuation of future cashflows cannot abstract away from the
contribution of the past. As a practical application, we provide an explicit
expression for the market value of human capital in a setting with wage
rigidity
Stochastic Landau-Lifshitz-Gilbert equations for frustrated magnets under fluctuating currents
We examine a stochastic Landau-Lifshitz-Gilbert equation for a frustrated
ferromagnet with competing first and second order exchange interactions exposed
to deterministic and random spin transfer torques in form of transport noise.
We prove the existence and pathwise uniqueness of weak martingale solutions in
the energy space. The result ensures the persistence of topological patterns,
occurring in such magnetic systems, under the influence of a fluctuating spin
current