Quick search | Browse volumes | |

XXIX: 16, 166-180, LNM 1613 (1995)

**APPLEBAUM, David**

A horizontal Lévy process on the bundle of orthonormal frames over a complete Riemannian manifold (Stochastic differential geometry, Markov processes)

This is an attempt to define a manifold-valued Lévy process by solving a SDE driven by a Euclidean Lévy process; but the author shows that the so-obtained processes are not Markovian in general.

Comment: The existence and uniqueness statements are a particular case of general theorems due to Cohen (*Stochastics Stochastics Rep.* **56**, 1996). The same question is addressed by Cohen in the next article 2917

Keywords: Semimartingales with jumps, Lévy processes, Infinitesimal generators

Nature: Original

Retrieve article from Numdam

XXIX: 17, 181-193, LNM 1613 (1995)

**COHEN, Serge**

Some Markov properties of stochastic differential equations with jumps (Stochastic differential geometry, Markov processes)

The Schwartz-Meyer theory of second-order calculus for manifold-valued continuous semimartingales (see 1505 and 1655) was extended by Cohen to càdlàg semimartingales (*Stochastics Stochastics Rep.* **56**, 1996). Here this language is used to study the Markov property of solutions to SDE's with jumps. In particular,two definitions of a Lévy process in a Riemannian manifold are compared: One as the solution to a SDE driven by some Euclidean Lévy process, the other by subordinating some Riemannian Brownian motion. It is shown that in general the former is not of the second kind

Comment: The first definition is independently introduced by David Applebaum 2916

Keywords: Semimartingales with jumps, Lévy processes, Subordination, Infinitesimal generators

Nature: Original

Retrieve article from Numdam

A horizontal Lévy process on the bundle of orthonormal frames over a complete Riemannian manifold (Stochastic differential geometry, Markov processes)

This is an attempt to define a manifold-valued Lévy process by solving a SDE driven by a Euclidean Lévy process; but the author shows that the so-obtained processes are not Markovian in general.

Comment: The existence and uniqueness statements are a particular case of general theorems due to Cohen (

Keywords: Semimartingales with jumps, Lévy processes, Infinitesimal generators

Nature: Original

Retrieve article from Numdam

XXIX: 17, 181-193, LNM 1613 (1995)

Some Markov properties of stochastic differential equations with jumps (Stochastic differential geometry, Markov processes)

The Schwartz-Meyer theory of second-order calculus for manifold-valued continuous semimartingales (see 1505 and 1655) was extended by Cohen to càdlàg semimartingales (

Comment: The first definition is independently introduced by David Applebaum 2916

Keywords: Semimartingales with jumps, Lévy processes, Subordination, Infinitesimal generators

Nature: Original

Retrieve article from Numdam