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 …

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

We consider stochastic differential equation $$ d X_t= b (X_t) dt+ d W_t^ H, $$ where the
drift $ b $ is either a measure or an integrable function, and $ W^ H $ is a $ d $-dimensional …

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

Our aim in this survey is to show how pseudodifferential operators arise naturally in the
theory of Markov processes and that this opens the way to use Fourier analytic techniques …

Abstract Let L:=-a(x)(-Δ)^α/2+(b(x),∇), where α∈(0,2), and a:R^d→(0,∞), b:R^d→R^d.
Under certain regularity assumptions on the coefficients a and b, we associate with the …

A SYMBOLIC CALCULUS FOR PSEUDO DIFFERENTIAL OPERATORS GENERATING FELLER
SEMIGROUPS Page 1 Hoh, W. Osaka J. Math. 35 (1998), 789-820 A SYMBOLIC CALCULUS …

In this paper, we study the following stochastic differential equation (SDE) in Rd: dXt= dZt+ b
(t, Xt) dt, X0= x, where Z is a Lévy process. We show that for a large class of Lévy processes …

Suppose that $ d\geq 1$ and $\alpha\in (1, 2) $. Let $\mathcal {L}^ b=-(-\Delta)^{\alpha/2}+
b\cdot\nabla $, where $ b $ is an $\mathbb {R}^ d $-valued measurable function on …