On Linear Stochastic Flows

2021/05/10 by Beniamin Gołdys, Goldys, Beniamin, Szymon Peszat +1 · 1 citation
Economics, Econometrics and Finance · Engineering · #Stochastic processes and financial applications #Reservoir Engineering and Simulation Methods #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.48550/arxiv.2105.04140

Abstract

We study the existence of the stochastic flow associated to a linear stochastic evolution equation d X= AX d t +∑_k B_k X d W_k, on a Hilbert space. Our first result covers the case where A is the generator of a C₀-semigroup, and (B_k) is a sequence of bounded linear operators such that ∑_k‖B_k‖

Cited by

• Generalized Ornstein-Uhlenbeck process for affine stochastic functional differential equations and its applications

Related

• On the Existence Theory of Hilbert Space valued Diffusion Processes
• Stochastic flows for Hölder drifts and transport/continuity equations with noise
• Stochastic Evolution Equations in Banach Spaces and Applications to Heath-Jarrow-Morton-Musiela Equation
• Stochastic evolution equations in UMD Banach spaces
• A note on stochastic semilinear dissipative evolution equations