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 note on the exponential stability of a matrix Riccati equation of stochastic control
A mathematical correction problem
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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