On the stability of infinite-dimensional linear stochastic systems
Professor Stefan Rolewicz: Curriculum vitae and List of publications
Stochastic invariance and consistency of financial models
The paper is devoted to a connection between stochastic invariance in infinite dimensions and a consistency question of mathematical finance. We derive necessary and sufficient conditions for stochastic invariance of Nagumo’s type for stochastic equations with additive noise. They are applied to Ornstein-Uhlenbeck processes and to specific financial models. The case of evolution equations with general noise is discussed also and a comparison with recent results obtained by geometric methods is presented...
A mathematical correction problem
A note on the exponential stability of a matrix Riccati equation of stochastic control
Stability properties of the discrete Riccati operator equation
Regularity of solutions to stochastic Volterra equations
We study regularity of stochastic convolutions solving Volterra equations on driven by a spatially homogeneous Wiener process. General results are applied to stochastic parabolic equations with fractional powers of Laplacian.
Contents
Differentiability of the Feynman-Kac semigroup and a control application
The Hamilton-Jacobi-Bellman equation corresponding to a large class of distributed control problems is reduced to a linear parabolic equation having a regular solution. A formula for the first derivative is obtained.
Continuity of stochastic convolutions
Let be a Brownian motion, and let be the space of all continuous periodic functions with period 1. It is shown that the set of all such that the stochastic convolution , does not have a modification with bounded trajectories, and consequently does not have a continuous modification, is of the second Baire category.
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