相关论文: On the Interpretation of Stratonovich Calculus
We study the stochastic stability in the zero-noise limit from a quantitative point of view. We consider smooth expanding maps of the circle, perturbed by additive noise. We show that in this case the zero-noise limit has a quadratic speed…
The abrupt changes that are ubiquitous in physical and natural systems are often well characterized by shot noise with a state dependent recurrence frequency and jump amplitude. For such state dependent behavior, we derive the transition…
We study weighted Tikhonov regularization for large-scale linear discrete ill-posed problems with random noise. Under a polynomial upper-bound assumption on the generalized eigenvalues of the discrete forward operator, we derive stochastic…
The zero-noise limit of differential equations with singular coefficients is investigated for the first time in the case when the noise is an $\alpha $-stable process. It is proved that extremal solutions are selected and the respective…
The diffusive dynamics of a particle in a medium with space-dependent friction coefficient is studied within the framework of the inertial Langevin equation. In this description, the ambiguous interpretation of the stochastic integral,…
Through certain appropriate constructions, we establish periodic solutions in distribution for some stochastic differential equations with infinite-dimensional Levy noise. Additionally, we obtain the corresponding periodic measures and…
Symmetries can be used to integrate scalar Ito equation -- or reduce systems of such equations -- by the Kozlov substitution, i.e. passing to symmetry adapted coordinates. While the theory is well established for so called deterministic…
Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…
The results of the author and Gess [27] develop a robust well-posedness theory for a broad class of conservative stochastic PDEs, with both probabilistically stationary and non-stationary Stratonovich noise, and with irregular noise…
We propose and analyse a novel, fully discrete numerical algorithm for the approximation of the generalised Stokes system forced by transport noise -- a prototype model for non-Newtonian fluids including turbulence. Utilising the Gradient…
Shot-Noise processes constitute a useful tool in various areas, in particular in finance. They allow to model abrupt changes in a more flexible way than processes with jumps and hence are an ideal tool for modelling stock prices, credit…
We study the estimation of moments and joint moments of microstructure noise. Estimators of arbitrary order of (joint) moments are provided, for which we establish consistency as well as central limit theorems. In particular, we provide…
Inverse Optimal Control (IOC) seeks to recover an unknown cost from expert demonstrations, and it provides a systematic way of modeling experts' decision mechanisms while considering the prior information of the cost functions.…
This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…
Multiplicative noise makes stochastic dynamics depend on how the white-noise limit is interpreted. In multidimensional systems with matrix-valued noise amplitudes $\sigma(x)$, this dependence includes a local Jacobian contribution that is…
We present a theoretical investigation of shot-noise properties in nondegenerate elastic diffusive conductors. Both Monte Carlo simulations and analytical approaches are used. Two new phenomena are found: (i) the display of enhanced shot…
We study the invariance of stochastic differential equations under random diffeomorphisms, and establish the determining equations for random Lie-point symmetries of stochastic differential equations, both in Ito and in Stratonovich form.…
We derive the Helmholtz theorem for stochastic Hamiltonian systems. Precisely, we give a theorem characterizing Stratonovich stochastic differential equations, admitting a Hamiltonian formulation. Moreover, in the affirmative case, we give…
A continuous-time Markowitz's mean-variance portfolio selection problem is studied in a market with one stock, one bond, and proportional transaction costs. This is a singular stochastic control problem,inherently in a finite time horizon.…
Our simple but useful technique is using an integration by parts to split the stochastic convolution into two terms. We develop five applications for this technique. The first one is getting a uniform estimate of stochastic convolution of…