"We present an approach that allows one to introduce a Malliavin type calculus for functionals of general Lévy processes and to obtain sufficient conditions for the absolute continuity of solutions of stochastic differential equations with jumps (we do not pose any assumptions about regularity of the intensity of the jumps). Our investigations are motivated by a pioneering idea due to Bismut ... and developed further by many authors. The idea is to extend the Malliavin approach to regularity of Wiener functionals to more general probability spaces by introducing a smooth structure in these spaces in terms of a “differentiation rule”, integration-by-parts formula, and by further applications of the stochastic calculus of variations to smooth functionals with nondegenerate derivatives."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
Alexey M. Kulik (as translated by Oleg Klesov):
https://en.wikiquote.org/wiki/Malliavin_calculus
Revision History
No revisions have been submitted for this quote.
Categories
Malliavin calculus
Malliavin calculus is a part of mathematical probability theory in which the calculus of variations is generalized to stochastic processes. The mathematical theory was introduced by Paul Malliavin in two fundamental papers, one in 1976 and the other in 1978.
5 quotes on TrueQuotesView all quotes by Malliavin calculus →
Related Quotes
"Denis R. Bell:"
"The mathematical theory now known as Malliavin calculus was first introduced by Paul Malliavin .. as an infinite-dime…"
"Malliavin’s work inspired many new results in stochastic analysis. Examples include filtering theorems (Michel ...), …"
"The Malliavin calculus refers to a part of Probability theory which can loosely be described as a type of calculus of…"
"The problem of three bodies has been treated in various ways since the time of Lagrange, but no decided advance towar…"
"We should speak of a dialectics of the calculus... the problem element in so far as... distinguished from the properl…"
"In general, a differential equation arises whenever you have a quantity subject to change. ...Strictly speaking, the …"
"[W]e find an excellent tract by James Bernoulli concerning the elastic curve, isochronous curves, the path of mean di…"
"Newton] teaches us to take the s, of any given order, of an equation with any given number of variable quantities, wh…"
"I ought also to mention Jacobi]'s papers on Abelian transcendants; his investigations on the theory of numbers... his…"