Now in its second edition, this book gives a systematic and self-contained presentation of
basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and …

Lévy processes form a wide and rich class of random process, and have many applications
ranging from physics to finance. Stochastic calculus is the mathematics of systems …

Fix a domain\mathcal S ⊂ R^ k (our solvency region) and let Y (t)= Y^(u)(t) be a stochastic
process of the form d Y (t) &= b (Y (t), u (t)) d t+ σ (Y (t), u (t)) d B (t)\nonumber\&\quad+ ∫ …

We introduce affine Volterra processes, defined as solutions of certain stochastic
convolution equations with affine coefficients. Classical affine diffusions constitute a special …

The main objective of this book is to give an overview of the theory of Hamilton–Jacobi–
Bellman (HJB) partial differential equations (PDEs) in infinite-dimensional Hilbert spaces …

As a relatively new area in mathematics, stochastic partial differential equations (PDEs) are
still at a tender age and have not yet received much attention in the mathematical …

A nonlinear Markov evolution is a dynamical system generated by a measure-valued
ordinary differential equation with the specific feature of preserving positivity. This feature …

The general area of stochastic PDEs is interesting to mathematicians because it contains an
enormous number of challenging open problems. There is also a great deal of interest in this …

Partial differential equations (PDEs) with random input data, such as random loadings and
coefficients, are reformulated as parametric, deterministic PDEs on parameter spaces of …

Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial
differential equations with slow and fast time scales, or large and small spatial scales. The …