This monograph provides the most recent and up-to-date developments on fractional
differential and fractional integro-differential equations involving many different potentially …

This volume concentrates on how to construct a Markov process by starting with a suitable
pseudo-differential operator. Feller processes, Hunt processes associated with Lp-sub …

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 theory of parabolic equations, a well-developed part of the contemporary partial
differential equations and mathematical physics, is the subject theory of of an immense …

Provides comprehensive coverage of the most recent developments in the theory of non-
Archimedean pseudo-differential equations and its application to stochastics and …

This paper studies the Cauchy problem for the nonlinear fractional power dissipative
equation ut+ (−△) αu= F (u) for initial data in the Lebesgue space Lr (Rn) with either r≥ rd≜ …

Asymptotic expansions are obtained for finite-dimensional symmetric stable distributions.
They are used to prove the existence of continuous transition probability densities of stable …

In this volume two topics are discussed: the construction of Feller and Lp-sub-Markovian
semigroups by starting with a pseudo-differential operator, and the potential theory of these …

The monograph is devoted mainly to the analytical study of the differential, pseudo-
differential and stochastic evolution equations describing the transition probabilities of …

Let d\geqslant 1 d⩾ 1 and α ∈ (0, 2) α∈(0, 2). Consider the following non-local and non-
symmetric Lévy-type operator on\mathbb R^ d R d:^ κ _ α f (x):= pv ∫ _\mathbb R^ d (f (x+ z) …