35,441 research outputs found
Diffusion semigroup on manifolds with time-dependent metrics
Let , on a differential manifold equipped
with time-depending complete Riemannian metric , where
is the Laplacian induced by and is a
family of -vector fields. We first present some explicit criteria for
the non-explosion of the diffusion processes generated by ; then establish
the derivative formula for the associated semigroup; and finally, present a
number of equivalent semigroup inequalities for the curvature lower bound
condition, which include the gradient inequalities, transportation-cost
inequalities, Harnack inequalities and functional inequalities for the
diffusion semigroup
Stochastic differential games for fully coupled FBSDEs with jumps
This paper is concerned with stochastic differential games (SDGs) defined
through fully coupled forward-backward stochastic differential equations
(FBSDEs) which are governed by Brownian motion and Poisson random measure. For
SDGs, the upper and the lower value functions are defined by the controlled
fully coupled FBSDEs with jumps. Using a new transformation introduced in [6],
we prove that the upper and the lower value functions are deterministic. Then,
after establishing the dynamic programming principle for the upper and the
lower value functions of this SDGs, we prove that the upper and the lower value
functions are the viscosity solutions to the associated upper and the lower
Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations, respectively. Furthermore, for
a special case (when do not depend on ), under the
Isaacs' condition, we get the existence of the value of the game.Comment: 33 page
estimates for fully coupled FBSDEs with jumps
In this paper we study useful estimates, in particular -estimates, for
fully coupled forward-backward stochastic differential equations (FBSDEs) with
jumps. These estimates are proved at one hand for fully coupled FBSDEs with
jumps under the monotonicity assumption for arbitrary time intervals and on the
other hand for such equations on small time intervals. Moreover, the
well-posedness of this kind of equation is studied and regularity results are
obtained.Comment: 19 page
Stochastic Differential Games and Viscosity Solutions of Hamilton-Jacobi-Bellman-Isaacs Equations
In this paper we study zero-sum two-player stochastic differential games with
the help of theory of Backward Stochastic Differential Equations (BSDEs). At
the one hand we generalize the results of the pioneer work of Fleming and
Souganidis by considering cost functionals defined by controlled BSDEs and by
allowing the admissible control processes to depend on events occurring before
the beginning of the game (which implies that the cost functionals become
random variables), on the other hand the application of BSDE methods, in
particular that of the notion of stochastic "backward semigroups" introduced by
Peng allows to prove a dynamic programming principle for the upper and the
lower value functions of the game in a straight-forward way, without passing by
additional approximations. The upper and the lower value functions are proved
to be the unique viscosity solutions of the upper and the lower
Hamilton-Jacobi-Bellman-Isaacs equations, respectively. For this Peng's BSDE
method is translated from the framework of stochastic control theory into that
of stochastic differential games.Comment: The results were presented by Rainer Buckdahn at the "12th
International Symposium on Dynamic Games and Applications" in
Sophia-Antipolis (France) in June 2006; They were also reported by Juan Li at
2nd Workshop on "Stochastic Equations and Related Topics" in Jena (Germany)
in July 2006 and at one seminar in the ETH of Zurich in November 200
- …